# Definition:Correspondence

A relation $\RR \subseteq S \times T$ is a correspondence if and only if $\RR$ is both left-total and right-total.
Some sources, for example 1974: P.M. Cohn: Algebra: Volume $\text { 1 }$, define a correspondence as a relation with no restrictions upon it.
That is, a correspondence from $S$ to $T$ is any subset of the Cartesian product $S \times T$.