<?xml version="1.0" encoding="UTF-8"?>

<record version="15" id="1975">
 <title>mapping</title>
 <name>Mapping</name>
 <created>2002-02-15 07:40:15</created>
 <modified>2006-10-31 11:35:10</modified>
 <type>Definition</type>
<parent id="360">function</parent>
 <creator id="146" name="rmilson"/>
 <author id="3771" name="CWoo"/>
 <author id="146" name="rmilson"/>
 <classification>
	<category scheme="msc" code="03E20"/>
 </classification>
 <synonyms>
	<synonym concept="mapping" alias="map"/>
 </synonyms>
 <related>
	<object name="DirectImage"/>
	<object name="InverseImage"/>
	<object name="Domain"/>
	<object name="Codomain"/>
	<object name="Set"/>
	<object name="Function"/>
	<object name="Transformation"/>
 </related>
 <preamble>\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}


\newtheorem{proposition}{Proposition}</preamble>
 <content>\PMlinkescapeword{generic}
\PMlinkescapeword{term}
\PMlinkescapeword{field}
The term \emph{mapping} is a synonym of \PMlinkname{function}{Function}, although usage patterns suggest that  ``mapping'' is the more generic term.

In a geometric context, the term ``function'' often connotes a mapping whose purpose is to assign values to the elements of its domain. In other words, a function defines a field of values.  By contrast, ``mapping'' has a more geometric connotation, as in ``a mapping of one space to another''.</content>
</record>
