Definition:Codomain (Relation Theory)
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This page is about Codomain in the context of Set Theory. For other uses, see Codomain.
Definition
Relation
The codomain of a relation $\RR \subseteq S \times T$ is $T$.
It can be denoted $\Cdm \RR$.
Mapping
The term codomain is usually seen when the relation in question is actually a mapping:
Let $f: S \to T$ be a mapping.
The codomain of $f$ is $T$.
It is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ by $\Cdm f$.
Also known as
Some sources write codomain as co-domain.
Also see
- Definition:Domain (Relation Theory)
- Definition:Range of Relation
- Definition:Image (Relation Theory)
- Definition:Preimage
- Results about codomains' in the context of mapping theory and relation theory' can be found here.