Definition:Correspondence
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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 define a correspondence as a relation with no restrictions upon it.
That is, a correspondence from $S$ to $T$ is an arbitrary subset of the Cartesian product $S \times T$.
In order to reduce confusion, it is recommended that this usage of correspondence is not used.
Also see
- Results about correspondences can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): correspondence
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): correspondence