Definition:Extension of Relation

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 $\RR_1$.

Also see

 * Definition:Restriction of Relation


 * Definition:Extension of Mapping
 * Definition:Extension of Operation