# Set of Mappings can be Ordered by Inclusion

## Theorem

Let $S \times T$ be the product of two sets.

Let $\mathcal F$ be a set of mappings on $S \times T$.

Then $\mathcal F$ can be ordered by inclusion.

## Proof

By the definition of mapping, a mapping is a specific type of relation.

The result then follows from Set of Relations can be Ordered by Inclusion.

$\blacksquare$