extension of a function

Let $f:X\to Y$ be a function and $A$ and $B$ be sets such that $X\subseteq A$ and $Y\subseteq B$. An ^{Planetmath Planetmath} of $f$ to $A$ is a function $g:A\to B$ such that $f(x)=g(x)$ for all $x\in X$. Alternatively, $g$ is an extension of $f$ to $A$ if $f$ is the ^{Planetmath Planetmath} of $g$ to $X$.

Typically, functions are not arbitrarily extended. Rather, it is usually insisted upon that extensions have certain properties. Examples include analytic continuations and meromorphic extensions.

Title	extension of a function
Canonical name	ExtensionOfAFunction
Date of creation	2013年03月22日 17:51:00
Last modified on	2013年03月22日 17:51:00
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	6
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 03E20
Related topic	RestrictionOfAFunction
Defines	extension