Category:Examples of Extensions of Mappings

This category contains examples of 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 $f_2 \restriction_{X \times Y} = f_1$.

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

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