# extension of a function

Let $f\colon X\to Y$ be a function and $A$ and $B$ be sets such that $X\subseteq A$ and $Y\subseteq B$. An extension of $f$ to $A$ is a function $g\colon A\to B$ such that $f(x)=g(x)$ for all $x\in X$. Alternatively, $g$ is an extension of $f$ to $A$ if $f$ is the restriction 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 ExtensionOfAFunction 2013-03-22 17:51:00 2013-03-22 17:51:00 Wkbj79 (1863) Wkbj79 (1863) 6 Wkbj79 (1863) Definition msc 03E20 RestrictionOfAFunction extension