Definition:Domain (Relation Theory)

Relation
The domain of a relation $$\mathcal{R} \subseteq S \times T$$ is the set $$S$$ and can be denoted $$\operatorname {Dom} \left({\mathcal{R}}\right)$$.

Some sources, for example, define the domain as:
 * $$\operatorname{Dom} \left({\mathcal{R}}\right) = \left\{{s \in S \exists t \in \operatorname{Rng} \left({\mathcal{R}}\right): \left({s, t}\right) \in \mathcal{R}}\right\}$$

Mapping
The term domain is usually seen when the relation in question is actually a mapping.

In the context of mappings, the domain and the preimage of a mapping are the same set.

Some sources, for example, call the domain the departure set.

Also see

 * Range (or Codomain)
 * Image
 * Preimage