Please refer to the errata for this document, which may include some normative corrections.
See also translations.
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.
This document is an editors' copy that has no official standing.
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 W3C technical reports index at http://www.w3.org/TR/.
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.
This third edition is based on Unicode 8.0 and incorporates changes to Unicode since Unicode 5.2 and 6.3, on which the first and second editions of this document were based. Note these updates only affect the non normative descriptions of the Unicode blocks. There are no changes to the Normative entity definitions. It also has been updated and restructured slightly to note that [HTML5] now uses these definitions. and to more clearly highlight that the HTML-MathML entity set should be used in preference to the older ISO sets that are also defined in this document.
This document was produced by the W3C Math Working Group as a Recommendation and as part of the W3C Math Activity. The goals of the W3C Math Working Group are discussed in the W3C Math WG Charter. The authors of this document are W3C Math Working Group members.
Comments should be sent to the Public W3C Math mailing list (list archives; see also instructions). When sending an e-mail comment on the XML Entity Definitions for Characters, please put the text “XML-Entities” in the subject line, preferably like this: “[XML-Entities] …summary of comment ”.
This document was produced by a group operating under the 5 February 2004 W3C Patent Policy. W3C maintains a public list of any patent disclosures 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 Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.
Appendix B Changes details the changes since earlier versions of this document.
2 Sets of names
2.1 The HTML MathML entity set
2.2 Legacy Entity sets
3 Unicode Character Ranges for Scientific Documents
4 Mathematical Alphanumeric Characters
5 Entities for Negated and Variant Characters
5.1 Negated Mathematical Characters
5.2 Variant Mathematical Characters
A Special Considerations
A.3 Multiple Character Entities
B.1 Changes since 2014-04-10 (Second Edition Recommendation)
B.2 Changes between 2010-04-01 and 2014-04-10 (First and Second Edition Recommendations)
B.3 Changes between 2010-04-01 and 2010-02-11
B.4 Changes between 2010-02-11 and 2009-11-17
B.5 Changes between 2009-11-17 and 2008-07-21
B.6 Changes between 2008-07-21 and 2007-12-14
C Differences between these entities and earlier W3C DTDs
C.1 Differences from XHTML 1.0
C.2 Differences from MathML 2.0 (second edition)
D Source Files
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.
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.
Specifically, the entity names in the sets starting with the letters "iso" were first standardized in SGML ([SGML]) and updated in [ISO9573-13-1991]. The W3C Math Working Group has been invited to take over the maintenance and development of these sets by the original standards committee (ISO/IEC JTC1 SC34). The sets with names starting "mml" were first standardized in MathML [MathML2] and those starting with "xhtml" were first standardized in HTML [HTML4].
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, and many more names used for MathML. This means that this document can be viewed as an extension and final revision of Chapter 6 of the MathML 2.0 [MathML2] recommendation. Now it presents a completed listing harmonizing the known uses of character entity names in XML and HTML, together with defined mappings to Unicode.
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.
Historically the entity sets have been split into relatively small groups of related characters however for any new document type that is being defined it is strongly recommended that the combined htmlmathml set is used. This defines an identical set of names to the names built in to the HTML parser (derived from the same source materials as this document see D Source Files).
To incorporate the htmlmathml set into an XML DTD, a typical construct is:
<!ENTITY % htmlmathml-f PUBLIC "-//W3C//ENTITIES HTML MathML Set//EN//XML" "http://www.w3.org/2003/entities/2007/htmlmathml-f.ent" > %htmlmathml-f;
The public identifier should always be used verbatim, The system identifier should be changed to suit local requirements.
The entity set is available in two forms:
The information is also available in JSON format. The JSON arrays encode the entity names and mappings to Unicode and also a list of those entity references for which the HTML (but not XML) parser allows the trailing semicolon to be omitted. So
& may be used as well as
& when using HTML.
An XSLT2 stylesheet is available which performs the reverse mapping, replacing Unicode characters by entity references.
This specification defines mappings to Unicode of many sets of names that have been defined by earlier specifications.
We present two tables listing all the sets combined, first in Unicode order and then in alphabetic order:
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).
In addition to the stylesheets and entity files corresponding to each individual entity set, a combined stylesheet is provided, as well as a combined entity set, in two formats, as for the HTML MathML set described above.
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.
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.
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.
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.
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.
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.
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 [Unicode15], especially the discussion of Normalization Form C.
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.
Historically there has been much confusion and lack of agreement over variant forms for lower case epsilon.
This specification uses the definitions below. Note that the name epsilon is used for the character used in textual Greek (U+03B5) and varepsilon 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 theta, vartheta) but incompatible with the naming convention used in TeX, MathML2 and some earlier mappings of the ISO entity sets to Unicode.
|eacgr||isogrk2||=small epsilon, accent, Greek||U+03AD||GREEK SMALL LETTER EPSILON WITH TONOS|
|egr||isogrk1||=small epsilon, Greek||U+03B5||GREEK SMALL LETTER EPSILON|
|epsiv||isogrk3||/straightepsilon, small epsilon, Greek||U+03F5||GREEK LUNATE EPSILON SYMBOL|
|straightepsilon||mmlalias||alias ISOGRK3 epsiv|
|varepsilon||mmlalias||alias ISOGRK3 epsiv|
|bepsi||isoamsr||/backepsilon R: such that||U+03F6||GREEK REVERSED LUNATE EPSILON SYMBOL|
|backepsilon||mmlalias||alias ISOAMSR bepsi|
|b.epsi||isogrk4||small epsilon, Greek||U+1D6C6||MATHEMATICAL BOLD SMALL EPSILON|
|b.epsiv||isogrk4||variant epsilon||U+1D6DC||MATHEMATICAL BOLD EPSILON SYMBOL|
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.
|phi||isogrk3||/phi - small phi, Greek||U+03C6||GREEK SMALL LETTER PHI|
|phi||xhtml1-symbol||greek small letter phi|
|phgr||isogrk1||=small phi, Greek|
|straightphi||mmlalias||alias ISOGRK3 phiv||U+03D5||GREEK PHI SYMBOL|
|phiv||isogrk3||/varphi - straight phi|
|varphi||mmlalias||alias ISOGRK3 phiv|
|b.phi||isogrk4||small phi, Greek||U+1D6D7||MATHEMATICAL BOLD SMALL PHI|
|b.phiv||isogrk4||variant phi||U+1D6DF||MATHEMATICAL BOLD PHI SYMBOL|
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.
|fjlig||isopub||small fj ligature||U+0066 U+006A||fj ligature|
|ThickSpace||mmlextra||space of width 5/18 em||U+205F U+200A||space of width 5/18 em|
|race||isoamsb||reverse most positive, line below||U+223D U+0331||REVERSED TILDE with underline|
|acE||isoamsb||most positive, two lines below||U+223E U+0333||INVERTED LAZY S with double underline|
|DownBreve||mmlextra||breve, inverted (non-spacing)||U+0020 U+0311||COMBINING INVERTED BREVE|
|tdot||isotech||three dots above||U+0020 U+20DB||COMBINING THREE DOTS ABOVE|
|TripleDot||mmlalias||alias ISOTECH tdot|
|DotDot||isotech||four dots above||U+0020 U+20DC||COMBINING FOUR DOTS ABOVE|
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 fjlig 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.
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 ThickSpace 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.
The entities race and acE 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.
For reasons explained further in [Charmod-norm], 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 tdot, TripleDot and DotDot 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.
Source files updated to Unicode 8.0, affecting the character tables, but with no changes to generated entity files or stylesheets.
Source files updated to Unicode 6.3, affecting the character tables, but with no changes to generated entity files or stylesheets.
Source files updated Unicode 6.1 data on Arabic math alphabets (U+1EE??). Additional tables shown in Sections 3 and 4.
Section 2 Sets of names reorganized to highlight the
htmlmathml set which is used in MathML and HTML. Also link to XSL and JSON formats for the HTML MathML set.
Several example images improved, bringing them more in line with the Unicode reference images.
Various editorial improvements, including using Unicode U+1234 notation more consistently rather than displaying the internal IDs of the form U01234.
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.
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).
The entities xvee and xwedge had the correct Unicode assignments (U+22C1 and U+22C0) but the entity descriptions have been swapped, xvee is logical or and xwedge is logical and. This error in [ISO9573-13-1991] was reported in 1999, in a Proposed Technical Corrigendum, but not previously fixed. The entity files are unaffected by this change.
The entity NotGreaterFullEqual 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).
A sample catalog is now provided to redirect references to the entity files to copies on the local machine rather than the W3C server.
The html5-uppercase set is now documented.
The entities ohm and angst have changed to U+03A9 and U+00C5 to match NFC. See w3c bugzilla entry.
The entity race, 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.)
The entities bsolhsub and suphsol 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.
The source files have all been updated to match Unicode 5.2.
The entity ThickSpace 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.
The entity UnderBar maps to the spacing character _ rather than the combining character U+0332.
The entity OverBar maps to the spacing character U+203E (like the XHTML entity oline) rather than the macron character U+00AF.
The entities epsiv and varepsilon are now mapped to the epsilon symbol U+03F5 rather than being aliases for the entity epsilon, U+03B5.
The entities phiv and varphi are now mapped to the phi symbol U+03D5 rather than being aliases for the entity phi, U+03C6.
Differences between the XHTML entity definitions described here and the entity set described in the XHTML 1.0 DTD.
The current drafts of [HTML5] use entity definitions derived from this specification.
The differences between MathML 2 and the current entity definitions are listed below.
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.
[MathML3] uses the entity sets defined by this specification.
All data files used to construct the entity declarations, XSLT character maps, and HTML tables referenced from this document are available from http://www.w3.org/2003/entities/2007xml/.