Definition:Many-to-One Relation/Defined/Set

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Definition

Let $f \subseteq S \times T$ be a many-to-one relation.

Let $R \subseteq S$.


Then $f$ is defined on $R$ if and only if it is defined at all $r \in R$.

Equivalently, if and only if $R \subseteq \Dom f$, the domain of $f$.