Definition:Left-Total Relation

Definition
Let $\RR \subseteq S \times T$ be a relation.

Then $\RR$ is left-total :
 * $\forall s \in S: \exists t \in T: \tuple {s, t} \in \RR$

That is, every element of $S$ relates to some element of $T$.

Also see

 * Definition:Right-Total Relation
 * Inverse of Left-Total Relation is Right-Total


 * Definition:Serial Relation: an endorelation $\RR: S \to S$ which is left-total