# Definition:Correspondence

## Definition

A relation $\mathcal R \subseteq S \times T$ is a **correspondence** if and only if $\mathcal R$ is both left-total and right-total.

## Also defined as

Some sources, for example 1974: P.M. Cohn: *Algebra: Volume 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 $S \times T$.

In order to reduce confusion, it is recommended that this usage of **correspondence** is not used.