Definition:Correspondence

From ProofWiki
Jump to navigation Jump to search

Definition

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


Also defined as

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 $S \times T$.

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