Definition:Extension of Mapping

Definition
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 $f_2 \restriction_{X \times Y} = f_1$.

That is, let $f_1$ be a subset of $f_2$.

Then $f_2$ extends or is an extension of $f_1$.

Also see

 * Definition:Restriction of Mapping


 * Definition:Extension of Relation
 * Definition:Extension of Operation