Definition:Codomain (Relation Theory)

This page is about Codomain in the context of Set Theory. For other uses, see Codomain.

Definition

The codomain of a relation $\RR \subseteq S \times T$ is $T$.

It can be denoted $\Cdm \RR$.

The term codomain is usually seen when the relation in question is actually a mapping:

Let $S$ and $T$ be sets.

Let $f: S \to T$ be a mapping.

The codomain of $f$ is $T$.

It is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ by $\Cdm f$.

Some sources write codomain as co-domain.

Results about codomains' in the context of mapping theory and relation theory' can be found here.