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

(Redirected from Definition:Defined on Set)
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 $f$.