Editing Map (mathematics) (section)

==Maps as functions==
{{Main article|Function (mathematics)}}

In many branches of mathematics, the term ''map'' is used to mean a [[Function (mathematics)|function]],<ref>{{Cite web|url=https://www.math-only-math.com/functions-or-mapping.html|title=Functions or Mapping {{!}} Learning Mapping {{!}} Function as a Special Kind of Relation|website=Math Only Math|access-date=2019-12-06}}</ref><ref name=":0">{{Cite web|url=http://mathworld.wolfram.com/Map.html|title=Map|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-12-06}}</ref><ref>{{Cite web|url=https://www.encyclopedia.com/education/news-wires-white-papers-and-books/mapping-mathematical|title=Mapping, Mathematical {{!}} Encyclopedia.com|website=www.encyclopedia.com|access-date=2019-12-06}}</ref> sometimes with a specific property of particular importance to that branch. For instance, a "map" is a "[[continuous function]]" in [[topology]], a "[[Linear map|linear transformation]]" in [[linear algebra]], etc.

Some authors, such as [[Serge Lang]],<ref>{{cite book |first=Serge |last=Lang |title=Linear Algebra |edition=2nd |year=1971 |page=83 |publisher=Addison-Wesley |isbn=0-201-04211-8 }}</ref> use "function" only to refer to maps in which the [[codomain]] is a set of numbers (i.e. a subset of [[real numbers|'''R''']] or [[complex numbers|'''C''']]), and reserve the term ''mapping'' for more general functions.

Maps of certain kinds have been given specific names. These include [[homomorphism]]s in [[algebra]], [[isometries]] in [[geometry]], [[Operator (mathematics)|operators]] in [[Mathematical analysis|analysis]] and [[Group representation|representations]] in [[group theory]].<ref name=":1" />  

In the theory of [[dynamical system]]s, a map denotes an [[Discrete-time dynamical system|evolution function]] used to create [[Dynamical system#Maps|discrete dynamical systems]]. 

A ''partial map'' is a ''[[partial function]]''. Related terminology such as ''[[Domain of a function|domain]]'', ''[[codomain]]'', ''[[Injective function|injective]]'', and ''[[Continuous function|continuous]]'' can be applied equally to maps and functions, with the same meaning. All these usages can be applied to "maps" as general functions or as functions with special properties.