Definition:Extension/Relation

Definition

Let:

• $\mathcal R_1 \subseteq X \times Y$ be a relation on $X \times Y$
• $\mathcal R_2 \subseteq S \times T$ be a relation on $S \times T$
• $X \subseteq S$
• $Y \subseteq T$
• $\mathcal R_2 \restriction_{X \times Y}$ be the restriction of $\mathcal R_2$ to $X \times Y$.

Let $\mathcal R_2 \restriction_{X \times Y} = \mathcal R_1$.

Then $\mathcal R_2$ extends or is an extension of $\mathcal R_1$.

Also see

• Restriction of a Relation

• Extension of a Mapping
• Extension of an Operation