\begin{definition}[Definition:Extension of Mapping]
As a mapping is, by definition, also a relation, the definition of an '''extension of a mapping''' is the same as that for an extension of a relation:
Let:
:$f_1 \subseteq X \times Y$ be a mapping on $X \times Y$
:$f_2 \subseteq S \times T$ be a mapping on $S \times T$
:$X \subseteq S$
:$Y \subseteq T$
:$f_2 \restriction_{X \times Y}$ be the restriction of $f_2$ to $X \times Y$.
Let $f_2 \restriction_{X \times Y} = f_1$.
Then $f_2$ '''extends''' or '''is an extension of''' $f_1$.
\end{definition}