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<!DOCTYPE html
PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html lang="en"><head><title>XML Entity Definitions for Characters</title><style type="text/css">
.base {background-color: #EEEEEE;}
.kwlabel {font-weight:normal}
</style><link rel="stylesheet" type="text/css" href="http://www.w3.org/StyleSheets/TR/W3C-REC.css"></head><body><div class="head"><p><a href="http://www.w3.org/"><img src="http://www.w3.org/Icons/w3c_home" alt="W3C" height="48" width="72"></a></p>
<h1><a name="title" id="title"></a>XML Entity Definitions for Characters</h1>
<h2><a name="w3c-doctype" id="w3c-doctype"></a>W3C Recommendation 01 April 2010</h2><dl><dt>This version:</dt><dd>
<a href="http://www.w3.org/TR/2010/REC-xml-entity-names-20100401/">http://www.w3.org/TR/2010/REC-xml-entity-names-20100401/</a>
</dd><dt>Latest version:</dt><dd>
<a href="http://www.w3.org/TR/xml-entity-names/">http://www.w3.org/TR/xml-entity-names/</a>
</dd><dt>Previous version:</dt><dd>
<a href="http://www.w3.org/TR/2010/PR-xml-entity-names-20100211/">http://www.w3.org/TR/2010/PR-xml-entity-names-20100211/</a>
</dd><dt>Editors:</dt><dd>David Carlisle, NAG</dd><dd>Patrick Ion, Mathematical Reviews, American Mathematical Society</dd></dl><p>Please refer to the <a href="http://www.w3.org/2003/entities/2007xml/errata.html"><strong>errata</strong></a>
for this document, which may include some normative corrections.</p><p>See also <a href="http://www.w3.org/2005/11/Translations/Query?titleMatch=XML+Entity+definitions+for+Characters"><strong>translations</strong></a>.</p><p class="copyright"><a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> &copy; 1998-2010 <a href="http://www.w3.org/"><acronym title="World Wide Web Consortium">W3C</acronym></a><sup>&reg;</sup> (<a href="http://www.csail.mit.edu/"><acronym title="Massachusetts Institute of Technology">MIT</acronym></a>, <a href="http://www.ercim.eu/"><acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym></a>, <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved. W3C <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>, <a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a> and <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> rules apply.</p></div><hr><div>
<h2><a name="abstract" id="abstract"></a>Abstract</h2><p>
This document defines several sets of names, so that to each name is assigned
a Unicode character or sequence of characters.
Each of these sets is expressed as a file of XML entity declarations.
</p></div><div>
<h2><a name="status" id="status"></a>Status of this Document</h2><p><em> This section describes the status of this document at the time
of its publication. Other documents may supersede this document. A
list of current W3C publications and the latest revision of this
technical report can be found in the <a href="http://www.w3.org/TR/">W3C technical reports index</a> at
http://www.w3.org/TR/.</em>
</p><p>This document has been reviewed by W3C Members, by software
developers, and by other W3C groups and interested parties, and is
endorsed by the Director as a W3C Recommendation. It is a stable
document and may be used as reference material or cited from another
document. W3C's role in making the Recommendation is to draw attention
to the specification and to promote its widespread deployment. This
enhances the functionality and interoperability of the Web.</p><p>
This document was produced by the
<a href="http://www.w3.org/Math/">W3C Math Working Group</a>
as a Recommendation and as part of the W3C
<a href="http://www.w3.org/Math/Activity">Math Activity</a>.
The goals of the W3C Math Working Group are discussed in the
<a href="http://www.w3.org/Math/Documents/Charter2006.html"> W3C Math WG Charter</a>.
The authors of this document are W3C Math Working Group members.
</p><p>
Comments should be sent to the
<a href="mailto:www-math@w3.org">Public W3C Math mailing list</a>
(<a href="http://lists.w3.org/Archives/Public/www-math/">list archives</a>;
see also <a href="http://www.w3.org/Mail/Request">instructions</a>).
When sending an e-mail comment on the XML Entity Definitions for Characters, please
put the text &#8220;XML-Entities&#8221; in the subject line, preferably like this:
&#8220;[XML-Entities] &#8230;summary of comment &#8221;.
</p><p> This document was produced by a group operating under the
<a href="http://www.w3.org/Consortium/Patent-Policy-20040205/">5 February 2004 W3C Patent Policy</a>.
W3C maintains a
<a href="http://www.w3.org/2004/01/pp-impl/35549/status">
public list of any patent disclosures</a> made in connection with
the deliverables of the group; that page also includes instructions
for disclosing a patent. An individual who has actual knowledge of
a patent which the individual believes contains
<a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential Claim(s)</a>
must disclose the information in accordance with
<a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section 6 of the W3C Patent Policy</a>.
</p><p> Appendix <a href="#changes"><b>B Changes</b></a> details the changes since earlier versions of this document.</p></div><div class="toc">
<h2><a name="contents" id="contents"></a>Table of Contents</h2><p class="toc">1 <a href="#chars_intro">Introduction</a><br>2 <a href="#sets">Sets of names</a><br>3 <a href="#blocks">Unicode Character Ranges for Scientific Documents</a><br>4 <a href="#alphabets">Mathematical Alphanumeric Characters</a><br>5 <a href="#combining">Entities for Negated and Variant Characters</a><br>&nbsp;&nbsp;&nbsp;&nbsp;5.1 <a href="#chars_math-negated-tables">Negated Mathematical Characters</a><br>&nbsp;&nbsp;&nbsp;&nbsp;5.2 <a href="#chars_math-variant-tables">Variant
Mathematical Characters</a><br></p>
<h3><a name="appendices" id="appendices"></a>Appendices</h3><p class="toc">A <a href="#oddities">Special Considerations</a><br>&nbsp;&nbsp;&nbsp;&nbsp;A.1 <a href="#epsilon">Epsilon</a><br>&nbsp;&nbsp;&nbsp;&nbsp;A.2 <a href="#phi">Phi</a><br>&nbsp;&nbsp;&nbsp;&nbsp;A.3 <a href="#chars_math-multiple-tables">Multiple Character Entities</a><br>B <a href="#changes">Changes</a><br>&nbsp;&nbsp;&nbsp;&nbsp;B.1 <a href="#changes20100211">Changes since 2010-02-11</a><br>&nbsp;&nbsp;&nbsp;&nbsp;B.2 <a href="#changes20091117">Changes between 2010-02-11 and 2009-11-17</a><br>&nbsp;&nbsp;&nbsp;&nbsp;B.3 <a href="#changes20080721">Changes between 2009-11-17 and 2008-07-21</a><br>&nbsp;&nbsp;&nbsp;&nbsp;B.4 <a href="#changes20071214">Changes between 2008-07-21 and 2007-12-14</a><br>C <a href="#diffs">Differences between these entities and earlier W3C DTDs</a><br>&nbsp;&nbsp;&nbsp;&nbsp;C.1 <a href="#diff-xhtml1">Differences from XHTML 1.0</a><br>&nbsp;&nbsp;&nbsp;&nbsp;C.2 <a href="#diff-mathml2">Differences from MathML 2.0 (second edition)</a><br>D <a href="#source">Source Files</a><br>E <a href="#references">References</a><br></p></div><hr><div class="body"><div class="div1">
<h2><a name="chars_intro" id="chars_intro"></a>1 Introduction</h2><p>
Notation and symbols have proved very important for human communication,
especially in scientific documents. Mathematics has
grown in part because its notation continually changes toward being succinct
and suggestive. There have been many new signs
developed for use in mathematical notation, and
mathematicians have not held back from making use of many symbols
originally introduced elsewhere. The result is that
science in general, and particularly mathematics, makes use of
a very large collection of symbols. It is
difficult to write science fluently if these characters are not
available for use. It is difficult to read science if
corresponding glyphs are not available for presentation on specific
display devices. In the majority of cases it is preferable to store
characters directly as Unicode character data or as XML numeric
character references.
</p><p>However, in some environments it is more
convenient to use the ASCII input mechanism provided by XML entity
references. Many entity names are in common use, and this
specification aims to provide standard mappings to Unicode for each of
these names. It introduces no names that have not already been used in
earlier specifications. Note that these names are short mnemonic names
designed for input methods such as XML entity references, not the longer formal names
that form part of the Unicode standard.
</p><p>
Specifically, the entity names in the sets
starting with the letters "iso" were first standardized in SGML (<a href="#SGML">[SGML]</a>) and updated in <a href="#ISO9573-13-1991">[ISO9573-13-1991]</a>.
The W3C Math Working Group has been
invited to take over the maintenance and development of these sets by the
original standards committee (ISO/IECJTC1 SC34). The sets with names
starting "mml" were first standardized in
MathML <a href="#MathML2">[MathML2]</a> and those starting
with "xhtml" were first standardized in HTML <a href="#HTML4">[HTML4]</a>.
</p><p>This document is the result of years of employing entity names on the Web. There were
always a few named entities used for special characters in HTML, but a flood of new
names came with the symbols of mathematics. This means that this document can be
viewed as an extension and final revision of Chapter 6 of the MathML 2.0
<a href="#MathML2">[MathML2]</a> recommendation. Now it presents a completed listing harmonizing
the known uses of character entity names throughout the XML world and Unicode.
</p><p>Since there are so many character entity names, and the files specifying them
are resources that may be subject to frequent lookup, a template catalog file has also been
provided. Users are strongly encouraged to design their implementations so that
relevant entity name tables are cached locally, since it is not expected that
the listings provided with this specification will need changing for some long time.
</p></div><div id="setsdiv">
<h2><a name="sets" id="sets"></a>2 Sets of names</h2><p>This specification defines mappings to Unicode of many sets of names
that have been defined by earlier specifications.</p><p>We first present two tables listing all the sets combined, first in
Unicode order and then in alphabetic order:</p><ul><li>All in <a href="bycodes.html">Unicode order</a></li><li>All in <a href="byalpha.html">alphabetic order</a>.</li></ul><p>Then there come tables
documenting each of the entity sets. Each set has a link to the DTD
entity declaration for the corresponding entity set, and also a link
to an XSLT2 stylesheet that will implement a reverse mapping from
characters to entity names (this is, of course, only possible for entity names
that map to a single Unicode code point).
</p><ul><li><a href="isobox.html">isobox</a>&nbsp;&nbsp;Box and Line Drawing</li><li><a href="isocyr1.html">isocyr1</a>&nbsp;&nbsp;Russian Cyrillic</li><li><a href="isocyr2.html">isocyr2</a>&nbsp;&nbsp;Non-Russian Cyrillic</li><li><a href="isodia.html">isodia</a>&nbsp;&nbsp;Diacritical Marks</li><li><a href="isolat1.html">isolat1</a>&nbsp;&nbsp;Added Latin 1</li><li><a href="isolat2.html">isolat2</a>&nbsp;&nbsp;Added Latin 2</li><li><a href="isonum.html">isonum</a>&nbsp;&nbsp;Numeric and Special Graphic</li><li><a href="isopub.html">isopub</a>&nbsp;&nbsp;Publishing</li><li><a href="isoamsa.html">isoamsa</a>&nbsp;&nbsp;Added Math Symbols: Arrow Relations</li><li><a href="isoamsb.html">isoamsb</a>&nbsp;&nbsp;Added Math Symbols: Binary Operators</li><li><a href="isoamsc.html">isoamsc</a>&nbsp;&nbsp;Added Math Symbols: Delimiters</li><li><a href="isoamsn.html">isoamsn</a>&nbsp;&nbsp;Added Math Symbols: Negated Relations</li><li><a href="isoamso.html">isoamso</a>&nbsp;&nbsp;Added Math Symbols: Ordinary</li><li><a href="isoamsr.html">isoamsr</a>&nbsp;&nbsp;Added Math Symbols: Relations</li><li><a href="isogrk1.html">isogrk1</a>&nbsp;&nbsp;Greek Letters</li><li><a href="isogrk2.html">isogrk2</a>&nbsp;&nbsp;Monotoniko Greek</li><li><a href="isogrk3.html">isogrk3</a>&nbsp;&nbsp;Greek Symbols</li><li><a href="isogrk4.html">isogrk4</a>&nbsp;&nbsp;Alternative Greek Symbols</li><li><a href="isomfrk.html">isomfrk</a>&nbsp;&nbsp;Math Alphabets: Fraktur</li><li><a href="isomopf.html">isomopf</a>&nbsp;&nbsp;Math Alphabets: Open Face</li><li><a href="isomscr.html">isomscr</a>&nbsp;&nbsp;Math Alphabets: Script</li><li><a href="isotech.html">isotech</a>&nbsp;&nbsp;General Technical</li><li><a href="mmlextra.html">mmlextra</a>&nbsp;&nbsp;Additional MathML Symbols</li><li><a href="mmlalias.html">mmlalias</a>&nbsp;&nbsp;MathML Aliases</li><li><a href="xhtml1-lat1.html">xhtml1-lat1</a>&nbsp;&nbsp;Latin for HTML</li><li><a href="xhtml1-special.html">xhtml1-special</a>&nbsp;&nbsp;Special for HTML</li><li><a href="xhtml1-symbol.html">xhtml1-symbol</a>&nbsp;&nbsp;Symbol for HTML</li><li><a href="html5-uppercase.html">html5-uppercase</a>&nbsp;&nbsp;uppercase aliases for HTML</li><li><a href="predefined.html">predefined</a>&nbsp;&nbsp;Predefined XML</li></ul><p>In addition to the stylesheets and entity files corresponding
to each individual entity set, a <a href="http://www.w3.org/2003/entities/2007/entitynamesmap.xsl">combined
stylesheet</a> is provided, as well as two combined entity sets, each
in two formats. First as a small file that
references the individual entity sets listed above, and then as a
larger file that directly contains a definition of each entity,
with the definitions sorted in order of entity names, with
duplicates removed. The first set, <b>w3centities</b> includes
all the entity sets defined in this specification. the second,
<b>htmlmathml</b>, is a slightly smaller set just comprising the
entity sets included in HTML and MathML. These are the entities
most likely to work (due to cached DTD or built in entity support)
if used in a web context.</p><ul><li><a href="http://www.w3.org/2003/entities/2007/w3centities.ent">w3centities</a> W3C entities collection; referencing all entity sets listed above</li><li><a href="http://www.w3.org/2003/entities/2007/w3centities-f.ent">w3centities-f</a> the same set of entity definitions, expanded into a single file, with duplicates removed</li><li><a href="http://www.w3.org/2003/entities/2007/htmlmathml.ent">htmlmathml</a>
htmlmathml collection; referencing the entity sets used in HTML or MathML</li><li><a href="http://www.w3.org/2003/entities/2007/htmlmathml-f.ent">htmlmathml-f</a> the expanded set of HTML and MathML entity definitions</li></ul></div><div id="blocksdiv">
<h2><a name="blocks" id="blocks"></a>3 Unicode Character Ranges for Scientific Documents</h2><p>
Certain characters are of particular relevance to scientific document production. The following
tables display Unicode ranges containing the characters that are most used in mathematics.
</p><p>Note that each of the tables linked from this section contains 256 images and may take a
while to load if the images have not been cached locally.</p><ul><li><span>000</span> <a href="000.html">C0 Controls and Basic Latin, C1 Controls and Latin-1 Supplement</a></li><li><span>001</span> <a href="001.html">Latin Extended-A, Latin Extended-B</a></li><li><span>002</span> <a href="002.html">IPA Extensions, Spacing Modifier Letters</a></li><li><span>003</span> <a href="003.html">Combining Diacritical Marks, Greek and Coptic</a></li><li><span>004</span> <a href="004.html">Cyrillic</a></li><li><span>020</span> <a href="020.html">General Punctuation, Superscripts and Subscripts, Currency Symbols, Combining Diacritical Marks for Symbols</a></li><li><span>021</span> <a href="021.html">Letterlike Symbols, Number Forms, Arrows</a></li><li><span>022</span> <a href="022.html">Mathematical Operators</a></li><li><span>023</span> <a href="023.html">Miscellaneous Technical</a></li><li><span>024</span> <a href="024.html">Control Pictures, Optical Character Recognition, Enclosed Alphanumerics</a></li><li><span>025</span> <a href="025.html">Box Drawing, Block Elements, Geometric Shapes</a></li><li><span>026</span> <a href="026.html">Miscellaneous Symbols</a></li><li><span>027</span> <a href="027.html">Dingbats, Miscellaneous Mathematical Symbols-A, Supplemental Arrows-A</a></li><li><span>029</span> <a href="029.html">Supplemental Arrows-B, Miscellaneous Mathematical Symbols-B</a></li><li><span>02A</span> <a href="02A.html">Supplemental Mathematical Operators</a></li><li><span>02B</span> <a href="02B.html">Miscellaneous Symbols and Arrows</a></li><li><span>0FB</span> <a href="0FB.html">Alphabetic Presentation Forms, Arabic Presentation Forms-A</a></li><li><span>0FE</span> <a href="0FE.html">Variation Selectors, Vertical Forms, Combining Half Marks, CJK Compatibility Forms, Small Form Variants, Arabic Presentation Forms-B</a></li><li><span>1D4</span> <a href="1D4.html">Mathematical Alphanumeric Symbols</a></li><li><span>1D5</span> <a href="1D5.html">Mathematical Alphanumeric Symbols (continued)</a></li><li><span>1D6</span> <a href="1D6.html">Mathematical Alphanumeric Symbols (continued)</a></li><li><span>1D7</span> <a href="1D7.html">Mathematical Alphanumeric Symbols (continued)</a></li></ul></div><div id="alphabetsdiv">
<h2><a name="alphabets" id="alphabets"></a>4 Mathematical Alphanumeric Characters</h2><p>
Many of the entities defined by this specification relate to the
mathematical alphanumeric characters contained in the letter-like
symbols block of Unicode Plane 0, or in the Mathematical Alphanumeric Symbols
block in Unicode Plane 1. The following tables list all these symbols,
highlighting those that are not in Plane 1, and giving entity names
where appropriate.
</p><ul><li><a href="bold.html">Bold (Serif)</a></li><li><a href="italic.html">Italic or Slanted</a></li><li><a href="bold-italic.html">Bold Italic or Slanted</a></li><li><a href="double-struck.html">Double Struck (Open Face, Blackboard Bold)</a></li><li><a href="script.html">Script (or Calligraphic)</a></li><li><a href="bold-script.html">Bold Script</a></li><li><a href="fraktur.html">Fraktur</a></li><li><a href="bold-fraktur.html">Bold Fraktur</a></li><li><a href="sans-serif.html">Sans Serif</a></li><li><a href="bold-sans-serif.html">Bold Sans Serif</a></li><li><a href="sans-serif-italic.html">Slanted Sans Serif</a></li><li><a href="sans-serif-bold-italic.html">Slanted Bold Sans Serif</a></li><li><a href="monospace.html">Monospace</a></li></ul></div><div class="div1">
<h2><a name="combining" id="combining"></a>5 Entities for Negated and Variant Characters</h2><p>
Each of the entity definitions in a majority of the specification expands
to a single Unicode character. The definitions that expand to a sequence of
two or more characters are outlined in this section.
</p><div class="div2">
<h3><a name="chars_math-negated-tables" id="chars_math-negated-tables"></a>5.1 Negated Mathematical Characters</h3><p>
In addition to the Unicode Characters so far listed, one may use the
combining characters U+0338 (/),
U+20D2 (|) and
U+20E5 (\) to produce
negated or canceled forms of
characters. A combining character
should be placed immediately after its "base" character, with no
intervening markup or space, just as is the case for combining accents.
</p><p>
In principle, the negation characters may be applied to any Unicode
character, although fonts designed for mathematics typically have some
negated glyphs ready composed. A MathML renderer should be able to use
these pre-composed glyphs in these cases. A compound character code
either represents a UCS character that is already available, as in the
case of U+003D U+0338 which amounts to
U+2260, or it does not, as is the
case for U+2202 U+0338. The common cases of
negations, of the latter type,
that have been identified are listed in the tables.</p><ul><li><a href="U00338.html">combining long solidus overlay</a></li><li><a href="U020D2.html">combining long vertical line overlay</a></li><li><a href="U020E5.html">combining reverse solidus overlay</a></li></ul><p>
Note that it is the policy of the W3C and of Unicode that if a single
character is already defined for what can be achieved with a combining
character, that character must be used instead of the decomposed form.
It is also intended that no new single characters representing what
can be done by with existing compositions will be introduced.
For further information on these matters see
the Unicode Standard Annex 15, Unicode Normalization Forms
<a href="#Unicode15">[Unicode15]</a>, especially
the discussion of Normalization Form C.
</p></div><div class="div2">
<h3><a name="chars_math-variant-tables" id="chars_math-variant-tables"></a>5.2 Variant
Mathematical Characters</h3><p>
Unicode attempts to avoid having several character codes for simple
font variants. For a code point to be assigned there should be
more than a nuance in glyphs to be recorded. To record
variants worth noting there is a special character in
Unicode 3.2, U+FE00 (VARIATION SELECTOR-1), which
acts as a postfix modifier. However the legally allowed
combinations with this variation selector are restricted to a
list recorded as part of Unicode. The VARIATION SELECTOR-1
character may only be applied to the characters listed here.
The resulting combination is not regarded by Unicode as a separate
character, but a variation on the base character. Unicode aware systems
may render the combination as the base if the available fonts do not
support the variant glyph shape.
</p><ul><li><a href="U0FE00.html">variation selector-1</a></li></ul></div></div></div><div class="back"><div class="div1">
<h2><a name="oddities" id="oddities"></a>A Special Considerations</h2><div class="div2">
<h3><a name="epsilon" id="epsilon"></a>A.1 Epsilon</h3><p>Historically there has been much confusion and lack of
agreement over variant forms for lower case epsilon.</p><p>This specification uses the definitions below. Note that the
name <b>epsilon</b> is used for the character used in textual
Greek (U+03B5) and <b>varepsilon</b> used for the epsilon
symbol character more commonly used in mathematics
(U+03F5). Note that this usage is compatible with the naming of
similar pairs of characters (for example <b>theta</b>,
<b>vartheta</b>) but <em>incompatible</em> with the naming
convention used in TeX, MathML2 and some earlier mappings of the
ISO entity sets to Unicode.</p><table border="border"><thead><tr><th>Entity</th><th>Set</th><th>Description</th><th colspan="3">Unicode Character</th></tr></thead><tbody><tr><td>eacgr</td><td>isogrk2</td><td>=small epsilon, accent, Greek</td><td rowspan="1">U+03AD</td><td rowspan="1"><img height="32" width="32" src="glyphs/003/U003AD.png" alt="U003AD"></td><td rowspan="1">GREEK SMALL LETTER EPSILON WITH TONOS</td></tr><tr><td>egr</td><td>isogrk1</td><td>=small epsilon, Greek</td><td rowspan="3">U+03B5</td><td rowspan="3"><img height="32" width="32" src="glyphs/003/U003B5.png" alt="U003B5"></td><td rowspan="3">GREEK SMALL LETTER EPSILON</td></tr><tr><td>epsi</td><td>isogrk3</td><td>/epsilon</td></tr><tr><td>epsilon</td><td>xhtml1-symbol</td><td></td></tr><tr><td>epsiv</td><td>isogrk3</td><td>/straightepsilon, small epsilon, Greek</td><td rowspan="3">U+03F5</td><td rowspan="3"><img height="32" width="32" src="glyphs/003/U003F5.png" alt="U003F5"></td><td rowspan="3">GREEK LUNATE EPSILON SYMBOL</td></tr><tr><td>straightepsilon</td><td>mmlalias</td><td>alias ISOGRK3 epsiv</td></tr><tr><td>varepsilon</td><td>mmlalias</td><td>alias ISOGRK3 epsiv</td></tr><tr><td>bepsi</td><td>isoamsr</td><td>/backepsilon R: such that</td><td rowspan="2">U+03F6</td><td rowspan="2"><img height="32" width="32" src="glyphs/003/U003F6.png" alt="U003F6"></td><td rowspan="2">GREEK REVERSED LUNATE EPSILON SYMBOL</td></tr><tr><td>backepsilon</td><td>mmlalias</td><td>alias ISOAMSR bepsi</td></tr><tr><td>b.epsi</td><td>isogrk4</td><td>small epsilon, Greek</td><td rowspan="1">U+1D6C6</td><td rowspan="1"><img height="32" width="32" src="glyphs/1D6/U1D6C6.png" alt="U1D6C6"></td><td rowspan="1">MATHEMATICAL BOLD SMALL EPSILON</td></tr><tr><td>b.epsiv</td><td>isogrk4</td><td>variant epsilon</td><td rowspan="1">U+1D6DC</td><td rowspan="1"><img height="32" width="32" src="glyphs/1D6/U1D6DC.png" alt="U1D6DC"></td><td rowspan="1">MATHEMATICAL BOLD EPSILON SYMBOL</td></tr></tbody></table></div><div class="div2">
<h3><a name="phi" id="phi"></a>A.2 Phi</h3><p>The situation for phi is very similar to that of epsilon,
although with the further complication that early versions of
Unicode had the sample glyphs for U+03C6 and U+03D5 swapped
from the current usage, and some older fonts still in use follow
that older convention. The definitions used in this
specification are as listed below.</p><table border="border"><thead><tr><th>Entity</th><th>Set</th><th>Description</th><th colspan="3">Unicode Character</th></tr></thead><tbody><tr><td>phi</td><td>isogrk3</td><td>/phi - small phi, Greek</td><td rowspan="3">U+03C6</td><td rowspan="3"><img height="32" width="32" src="glyphs/003/U003C6.png" alt="U003C6"></td><td rowspan="3">GREEK SMALL LETTER PHI</td></tr><tr><td>phi</td><td>xhtml1-symbol</td><td>greek small letter phi</td></tr><tr><td>phgr</td><td>isogrk1</td><td>=small phi, Greek</td></tr><tr><td>straightphi</td><td>mmlalias</td><td>alias ISOGRK3 phiv</td><td rowspan="3">U+03D5</td><td rowspan="3"><img height="32" width="32" src="glyphs/003/U003D5.png" alt="U003D5"></td><td rowspan="3">GREEK PHI SYMBOL</td></tr><tr><td>phiv</td><td>isogrk3</td><td>/varphi - straight phi</td></tr><tr><td>varphi</td><td>mmlalias</td><td>alias ISOGRK3 phiv</td></tr><tr><td>b.phi</td><td>isogrk4</td><td>small phi, Greek</td><td rowspan="1">U+1D6D7</td><td rowspan="1"><img height="32" width="32" src="glyphs/1D6/U1D6D7.png" alt="U1D6D7"></td><td rowspan="1">MATHEMATICAL BOLD SMALL PHI</td></tr><tr><td>b.phiv</td><td>isogrk4</td><td>variant phi</td><td rowspan="1">U+1D6DF</td><td rowspan="1"><img height="32" width="32" src="glyphs/1D6/U1D6DF.png" alt="U1D6DF"></td><td rowspan="1">MATHEMATICAL BOLD PHI SYMBOL</td></tr></tbody></table></div><div class="div2">
<h3><a name="chars_math-multiple-tables" id="chars_math-multiple-tables"></a>A.3 Multiple Character Entities</h3><p>
In addition to the combining and variant character combinations
listed in the previous sections,
the following table lists the remaining entity replacement texts that
consist of more than one character.
</p><table border="1"><thead><tr><th>Entity</th><th>Set</th><th>Description</th><th colspan="3">Unicode Character</th></tr></thead><tbody><tr class="combine"><td>fjlig</td><td>isopub</td><td>small fj ligature</td><td rowspan="1">U+0066 U+006A</td><td rowspan="1"><img height="32" width="32" src="glyphs/000/U00066-0006A.png" alt="U00066-0006A"></td><td rowspan="1">fj ligature</td></tr><tr class="combine"><td>ThickSpace</td><td>mmlextra</td><td>space of width 5/18 em</td><td rowspan="1">U+205F U+200A</td><td rowspan="1"><img height="32" width="32" src="glyphs/020/U0205F-0200A.png" alt="U0205F-0200A"></td><td rowspan="1">space of width 5/18 em</td></tr><tr class="combine"><td>race</td><td>isoamsb</td><td>reverse most positive, line below</td><td rowspan="1">U+223D U+0331</td><td rowspan="1"><img height="32" width="32" src="glyphs/022/U0223D-00331.png" alt="U0223D-00331"></td><td rowspan="1">REVERSED TILDE with underline</td></tr><tr class="combine"><td>acE</td><td>isoamsb</td><td>most positive, two lines below</td><td rowspan="1">U+223E U+0333</td><td rowspan="1"><img height="32" width="32" src="glyphs/022/U0223E-00333.png" alt="U0223E-00333"></td><td rowspan="1">INVERTED LAZY S with double underline</td></tr><tr class="combine"><td>DownBreve</td><td>mmlextra</td><td>breve, inverted (non-spacing)</td><td rowspan="1">U+0020 U+0311</td><td rowspan="1"><img height="32" width="32" src="glyphs/003/U00311.png" alt="U00311"></td><td rowspan="1">COMBINING INVERTED BREVE</td></tr><tr class="combine"><td>tdot</td><td>isotech</td><td>three dots above</td><td rowspan="2">U+0020 U+20DB</td><td rowspan="2"><img height="32" width="32" src="glyphs/020/U020DB.png" alt="U020DB"></td><td rowspan="2">COMBINING THREE DOTS ABOVE</td></tr><tr class="combine"><td>TripleDot</td><td>mmlalias</td><td>alias ISOTECH tdot</td></tr><tr class="combine"><td>DotDot</td><td>isotech</td><td>four dots above</td><td rowspan="1">U+0020 U+20DC</td><td rowspan="1"><img height="32" width="32" src="glyphs/020/U020DC.png" alt="U020DC"></td><td rowspan="1">COMBINING FOUR DOTS ABOVE</td></tr></tbody></table><p>Unicode does not have an fj character, although the other common f ligatures
such as fi (U+FB01) are contained in the Alphabetic Presentation Forms block.
The <b>fjlig</b> entity is mapped to the pair of characters "fj";
modern typesetting engines should automatically use the fj ligature for this
combination if the font supplies such a ligature.</p><p>Unicode has a range of space characters (including all multiples of
1/18 em up to 6/18, except for 5/18 em) thus the <b>ThickSpace</b> entity is
mapped to a pair of space characters. An alternative would have been to use
U+2005 (1/4 em), but 1/4 em is not equal to 5/18 em, so the above definition was
chosen, despite the fact that the difference is unlikely to be visibly
noticeable at most typeset font sizes.</p><p>The entities <b>race</b> and <b>acE</b> denote underlined
characters for which Unicode does not have codepoints, thus combining
underline characters have been used, in a way analogous to the use of
combining strokes for negated operators.</p><p>For reasons explained further in <a href="#Charmod-norm">[Charmod-norm]</a>, it is
not advisable to to start the replacement text of an entity with a
combining character, as then potentially different results may be
produced depending on the order in which entity expansion and Unicode
normalisation are performed. As far as possible this specification
uses non-combining characters, however, in the cases <b>tdot</b>,
<b>TripleDot</b> and <b>DotDot</b>
Unicode only has combining forms of the accents, and so the entity
replacement text starts with a space, to avoid the possibility that
the expansion of the entity combines with preceding text.</p></div></div><div class="div1">
<h2><a name="changes" id="changes"></a>B Changes</h2><div class="div2">
<h3><a name="changes20100211" id="changes20100211"></a>B.1 Changes since 2010-02-11</h3><p>Several example images improved, bringing them more in line with the Unicode reference images.</p></div><div class="div2">
<h3><a name="changes20091117" id="changes20091117"></a>B.2 Changes between 2010-02-11 and 2009-11-17</h3><p>Various editorial improvments, including using Unicode U+1234
notation more consistently rather than displaying the internal
IDs of the form U01234.</p><p>The combined entities file distributed with the 2009-11-17
draft introduced an error that if two entity names differed only
by case, only one was included. This has been corrected.</p><p>The combined entity set htmlmathml corresponding to the
entities usable in HTML and MathML is now explicitly provided. The
predefined set, corresponding to the entities predefined in XML
is now documented (it was previously used internally).</p><p>The entities <b>xvee</b> and <b>xwedge</b> had the correct
Unicode assignments (U+22C1 and U+22C0) but the entity descriptions
have been swapped, <b>xvee</b> is logical or and <b>xwedge</b> is logical and.
This error in <a href="#ISO9573-13-1991">[ISO9573-13-1991]</a> was reported in 1999,
<a href="http://www.jtc1sc34.org/repository/0063.htm">Proposed Technical Corrigendum</a>
but not previously fixed. The entity files are unaffected by this change.</p><p>The entity <b>NotGreaterFullEqual</b> which had been erroneously assigned to
a negated less than operator (U+2266 U+0338) has been corrected to be the negated greater than operator (U+2267 U+0338).</p><p>A sample <a href="#catalog">catalog</a> is now provided to redirect references to the entity files to copies on the local machine rather than the W3C server.</p></div><div class="div2">
<h3><a name="changes20080721" id="changes20080721"></a>B.3 Changes between 2009-11-17 and 2008-07-21</h3><p>The html5-uppercase set is now documented.</p><p>The entities <b>ohm</b> and <b>angst</b> have changed to U+03A9 and U+00C5 to match NFC. See
<a href="http://www.w3.org/Bugs/Public/show_bug.cgi?id=5897">w3c bugzilla entry</a>.</p><p>The entity <b>race</b>, which had been erroneously assigned U+29DA,
is now assigned the combination U+223D U+0331. (U+223D isn't
quite the shape shown in the original ISO document which is a
rotated S rather than a rotated tilde, but this appears to be
the closest character in Unicode 5.2.)</p><p>The entities <b>bsolhsub</b> and <b>suphsol</b> which were previously
mapped to two-character combinations U+005C U+2282 and U+2283 U+002F
are now mapped to the Unicode 5 characters that were added
specifically to support these entities, U+27C8 and U+27C9.</p><p>The source files have all been updated to match Unicode 5.2.</p><p>The entity <b>ThickSpace</b> now maps to the pair
U+205F U+200A rather than the triple U+2009 U+200A U+200A
(4/18 + 1/18)em rather than (3/18 + 1/18 + 1/18)em.</p><p>The entity <b>UnderBar</b> maps to the spacing character
_ rather than the combining character U+0332.</p><p>The entity <b>OverBar</b> maps to the spacing character
U+203E (like the XHTML entity <b>oline</b>) rather than the macron character U+00AF.</p><p>The entities <b>epsiv</b> and <b>varepsilon</b> are now mapped to the epsilon symbol
U+03F5 rather than being aliases for the entity <b>epsilon</b>, U+03B5.</p><p>The entities <b>phiv</b> and <b>varphi</b> are now mapped to the phi symbol U+03D5
rather than being aliases for the entity <b>phi</b>, U+03C6.</p></div><div class="div2">
<h3><a name="changes20071214" id="changes20071214"></a>B.4 Changes between 2008-07-21 and 2007-12-14</h3><p>The following entity definitions have changed at this draft:</p><p><b>phi</b>, <b>lang</b>, <b>rang</b>,
<b>OverParenthesis</b>, <b>UnderParenthesis</b>,
<b>OverBrace</b>, <b>UnderBrace</b>,
<b>lbbrk</b>, <b>rbbrk</b>.</p></div></div><div class="div1">
<h2><a name="diffs" id="diffs"></a>C Differences between these entities and earlier W3C DTDs</h2><div class="div2">
<h3><a name="diff-xhtml1" id="diff-xhtml1"></a>C.1 Differences from XHTML 1.0</h3><p>Differences between the XHTML entity definitions described here and the entity set
described in the <a href="http://www.w3.org/TR/xhtml1/dtds.html">XHTML 1.0 DTD</a>.</p><dl><dt class="kwlabel"><b>lang</b> and <b>rang</b></dt><dd>U+27E8 and
U+27E9; XHTML 1.0 used U+2329 and U+232A (which have canonical
decomposition to U+3008 and U+3009).</dd></dl><div class="note"><p class="prefix"><b>Note:</b></p><p>The current drafts of <a href="#HTML5">[HTML5]</a> use entity definitions derived from
this specification.</p></div></div><div class="div2">
<h3><a name="diff-mathml2" id="diff-mathml2"></a>C.2 Differences from MathML 2.0 (second edition)</h3><p>The differences between MathML 2 and the current entity
definitions are listed below.</p><dl><dt class="kwlabel"><b>fjlig</b></dt><dd>ISOPUB (and MathML 1) defined an fj ligature;
Unicode does not have a specific character and the entity was dropped from MathML2.
It is re-instated here for maximum compatibility with <a href="#SGML">[SGML]</a>.</dd><dt class="kwlabel"><b>phi</b></dt><dd>U+03C6 GREEK SMALL LETTER PHI
(the definition used in HTML4);
MathML2 used U+03D5 GREEK PHI SYMBOL. </dd><dt class="kwlabel"><b>epsiv</b>, <b>varepsilon</b>, <b>phiv</b>,
<b>varphi</b></dt><dd>these have been changed to map to the symbol character
(to match other uses of the var prefix such as <b>vartheta</b>).</dd><dt class="kwlabel"><b>jmath</b></dt><dd>U+0237; MathML 2 used U+006A (j) as
there was no dotless j before Unicode 4.1.</dd><dt class="kwlabel"><b>trpezium</b>, <b>elinters</b></dt><dd>U+23E2 and U+23E7;
MathML 2 used U+FFFD (REPLACEMENT CHARACTER) as these characters were added at Unicode 5.0
specifically to support these entities. </dd><dt class="kwlabel"><b>ohm</b>, <b>angst</b></dt><dd>As noted above, the
definitions of these entities have been changed so that the
definitions use characters that are in NFC normal
form.</dd><dt class="kwlabel"><b>bsolhsub</b> and <b>suphsol</b></dt><dd> U+27C8 and
U+27C9;
MathML2 used U+005C U+02282 and U+2283 U+002F.</dd><dt class="kwlabel"><b>NotGreaterFullEqual</b></dt><dd> U+2267 U+0338 ;
MathML2 used the erroneous definition U+2266 U+0338.</dd></dl><p>The following bracket symbols have been added to the Mathematical
symbols block in Unicode versions between 3.1 and 5.1. MathML2 used
similar characters intended for CJK punctuation.</p><dl><dt class="kwlabel"><b>lang</b>, <b>langle</b>, <b>LeftAngleBracket</b> and
<b>rang</b>, <b>rangle</b>, <b>RightAngleBracket</b></dt><dd>U+27E8 and
U+27E9; MathML2 used U+2329 and U+232A (which have canonical
decomposition to U+3008 and U+3009).</dd><dt class="kwlabel"><b>Lang</b> and <b>Rang</b></dt><dd>U+27EA and U+27EB;
MathML2 used U+300A and U+300B.</dd><dt class="kwlabel"><b>lbbrk</b> and <b>rbbrk</b></dt><dd>U+2772 and
U+2773; MathML2 used U+3014 and U+3015.</dd><dt class="kwlabel"><b>loang</b> and <b>roang</b></dt><dd>U+27EC and
U+27ED; MathML2 used U+3018 and U+3019.</dd><dt class="kwlabel"><b>lobrk</b> and <b>robrk</b></dt><dd>U+27E6 and
U+27E7; MathML2 used U+301A and U+301B.</dd><dt class="kwlabel"><b>OverBrace</b> and <b>UnderBrace</b></dt><dd>U+23DE and U+23DF; MathML2
used U+FE37 and U+FE38.</dd><dt class="kwlabel"><b>OverParenthesis</b> and
<b>UnderParenthesis</b></dt><dd>U+23DC and U+23DD;
MathML2 used U+FE35 and U+FE36.</dd><dt class="kwlabel"><b>LeftDoubleBracket</b> and
<b>RightDoubleBracket</b></dt><dd>U+27E6 and U+27E7;
MathML2 used U+301A and U+301B.</dd></dl><div class="note"><p class="prefix"><b>Note:</b></p><p><a href="#MathML3">[MathML3]</a> uses the entity sets defined by this specification, so there
will be no differences between MathML and the entities defined here once MathML3 is
finalized.</p></div></div></div><div class="div1">
<h2><a name="source" id="source"></a>D Source Files</h2><p>All data files used to construct the entity declarations, XSLT character maps, and
HTML tables referenced from this document are available from
<a href="http://www.w3.org/2003/entities/2007xml/">http://www.w3.org/2003/entities/2007xml/</a>.</p><p>
</p><ul><li><a href="http://www.w3.org/2003/entities/2007xml/unicode.xml">unicode.xml</a> master file detailing all Unicode characters with names in various entity sets and applications, TeX equivalents and other data. This file has been maintained for many years, originally by Sebastian Rahtz as part of the jadetex distribution and since around 1999 as part of the MathML specification sources by David Carlisle. The current version encodes data for all characters in Unicode 5.2.
<em>Note: unicode.xml is over 5MB in size and may not really be suitable for direct viewing in a browser. You may prefer to save the file rather than follow the above link to unicode.xml in a browser.</em></li><li><a href="http://www.w3.org/2003/entities/2007xml/charlist.rnc">charlist.rnc</a> relax NG schema for unicode.xml.</li><li><a href="http://www.w3.org/2003/entities/2007xml/unicode.xsl">unicode.xsl</a> XSLT stylesheet that renders unicode.xml as an HTML table.</li><li><a href="http://www.w3.org/2003/entities/2007xml/character-set.xml">character-set.xml</a> the source file for this document.</li><li><a href="http://www.w3.org/2003/entities/2007xml/xmlspec.xsl">xmlspec.xsl</a> a copy of the standard xmlspec stylesheet.</li><li><a href="http://www.w3.org/2003/entities/2007xml/run">run</a> small script file that builds this collection.</li><li><a href="http://www.w3.org/2003/entities/2007xml/xhtml1.xml">xhtml1.xml</a> record of XHTML 1.0 entity definitions.</li><li><a href="http://www.w3.org/2003/entities/2007xml/mml2.xml">mml2.xml</a> record of MathML 2.0 (second edition) entity definitions.</li><li><a href="http://www.w3.org/2003/entities/2007xml/unicodedata.xsl">unicodedata.xsl</a> stylesheet that generates a new copy of unicode.xml, incorporating data from the Unicode data file, used to update unicode.xml as new versions of Unicode are released.</li><li><a href="http://www.w3.org/2003/entities/2007xml/entities.xsl">entities.xsl</a> stylesheet to generate the DTD declarations for the entities.</li><li><a href="http://www.w3.org/2003/entities/2007xml/charmap.xsl">charmap.xsl</a> stylesheet to generate the XSLT character maps.</li><li><a href="http://www.w3.org/2003/entities/2007xml/characters.xsl">characters.xsl</a> stylesheet to generate this document, including the referenced HTML tables.</li><li><a href="http://www.w3.org/2003/entities/2007xml/schemas.xml">schemas.xml</a> file associating XML documents with appropriate Relax NG schema.</li><li id="catalog"><a href="http://www.w3.org/2003/entities/2007xml/catalog">catalog</a> Sample OASIS XML catalog that redirects references to the entity or stylesheet files at http://www.w3.org/2003/entities/2007/ to the local file system at
/etc/xml/w3c-entities. It should be edited to refer to the location of a local copy of the files. Many XML parsers may be configured to read this catalog format, but the specific options depend on the parser being used.</li></ul></div><div class="div1">
<h2><a name="references" id="references"></a>E References</h2><dl><dt class="label"><a name="SGML" id="SGML"></a>SGML</dt><dd>ISO/IEC 8879:1986, Information processing &#8212; Text and office
systems &#8212; Standard Generalized Markup Language (SGML)</dd><dt class="label"><a name="ISO9573-13-1991" id="ISO9573-13-1991"></a>ISO9573-13-1991</dt><dd>ISO/IEC TR :1991, Information
technology &#8212; SGML support facilities
Techniques for using
SGML &#8212; Part 13: Public entity sets for
mathematics and science</dd><dt class="label"><a name="Unicode" id="Unicode"></a>Unicode</dt><dd>The Unicode Consortium. The Unicode Standard, Version 5.2.0, defined by:
The Unicode Standard, Version 5.2 (Mountain View, CA: The Unicode Consortium, 2009. ISBN 978-1-936213-00-9).
(<a href="http://www.unicode.org/versions/Unicode5.0.0/">http://www.unicode.org/versions/Unicode5.2.0/</a>)
</dd><dt class="label"><a name="Unicode15" id="Unicode15"></a>Unicode15</dt><dd>Unicode Standard Annex 15, Version 5.2.0;
<em><a href="http://www.unicode.org/reports/tr15/tr15-31.html">Unicode Normalization Forms</a></em>,
The Unicode Consortium, 2009-09-03.
(<a href="http://www.unicode.org/reports/tr15/tr15-31.html">http://www.unicode.org/reports/tr15/tr15-31.html</a>)
</dd><dt class="label"><a name="Unicode25" id="Unicode25"></a>Unicode25</dt><dd>Barbara Beeton, Asmus Freytag, Murray Sargent III,
<em><a href="http://www.unicode.org/unicode/reports/tr25/">Unicode Support for Mathematics</a></em>,
Unicode Technical Report #25 2008-08-14.
(<a href="http://www.unicode.org/unicode/reports/tr25/">http://www.unicode.org/unicode/reports/tr25/</a>)
</dd><dt class="label"><a name="MathML2" id="MathML2"></a>MathML2</dt><dd>David Carlisle, Patrick Ion, Robert Miner, Nico Poppelier,
<em><a href="http://www.w3.org/TR/MathML2/">Mathematical Markup Language (MathML)
Version 2.0 (Second Edition)</a></em>
W3C Recommendation 21 October 2003
(<a href="http://www.w3.org/TR/2003/REC-MathML2-20031021/">http://www.w3.org/TR/2003/REC-MathML2-20031021/</a>)
</dd><dt class="label"><a name="MathML3" id="MathML3"></a>MathML3</dt><dd>David Carlisle, Patrick Ion, Robert Miner,
<em><a href="http://www.w3.org/TR/MathML3/">Mathematical Markup Language (MathML) Version 3.0</a></em>
W3C Candidate Recommendation 15 December 2009
(<a href="http://www.w3.org/TR/2009/CR-MathML3-20091215/">http://www.w3.org/TR/2009/CR-MathML3-20091215/</a>)
</dd><dt class="label"><a name="HTML4" id="HTML4"></a>HTML4</dt><dd>Dave Raggett, Arnaud Le Hors, Ian Jacobs,
<em><a href="http://www.w3.org/TR/html4/"></a>HTML 4.01 Specification</em>
W3C Recommendation 24 December 1999
(<a href="http://www.w3.org/TR/1999/REC-html401-19991224/">http://www.w3.org/TR/1999/REC-html401-19991224</a>)</dd><dt class="label"><a name="HTML5" id="HTML5"></a>HTML5</dt><dd>Ian Hickson, David Hyat,
<em><a href="http://www.w3.org/TR/html5/">HTML 5,
A vocabulary and associated APIs for HTML and XHTML</a></em>
W3C Working Draft 25 August 2009
(<a href="http://www.w3.org/TR/html5/">http://www.w3.org/TR/html5/</a>)</dd><dt class="label"><a name="Charmod-norm" id="Charmod-norm"></a>Charmod-norm</dt><dd> Fran&ccedil;ois Yergeau,
Martin J. D&uuml;rst,
Richard Ishida,
Addison Phillips,
Misha Wolf,
Tex Texin,
<em><a href="http://www.w3.org/TR/charmod-norm/">Character Model
for the World Wide Web 1.0: Normalization</a></em>
W3C Working Draft 27 October 2005
(<a href="http://www.w3.org/TR/charmod-norm/">http://www.w3.org/TR/charmod-norm/</a>)
</dd></dl></div></div></body></html>