Definition:Extension of Relation

This page is about extensions of relations. For other uses, see Extension.

Definition

Let:

$\RR_1 \subseteq X \times Y$ be a relation on $X \times Y$

$\RR_2 \subseteq S \times T$ be a relation on $S \times T$

$X \subseteq S$

$Y \subseteq T$

$\RR_2 \restriction_{X \times Y}$ be the restriction of $\RR_2$ to $X \times Y$.

Let $\RR_2 \restriction_{X \times Y} = \RR_1$.

Then $\RR_2$ extends or is an extension of $\RR_1$.