Definition:Many-to-One Relation/Defined/Subclass
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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 $f$.
Sources
- 1989: George S. Boolos and Richard C. Jeffrey: Computability and Logic (3rd ed.) ... (previous): $1$ Enumerability