Definition:Extension of Mapping

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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:


$f_1 \subseteq X \times Y$ 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 $f_1$.

Also see