Example 1

Let E, F be two sets, and let $\Phi(E, F)$ be the set of all mappings of subsets of E into F. For each $f \in \Phi(E, F)$ let $G_f$ be the graph of $f$, which is a subset of $E \times F$. If we endow $\Phi(E, F)$ with the order relation "*g extends f*" between $f$ and $g$ (no. 1, Example 3), then $f \to G_f$ is an isomorphism of the ordered set $\Phi(E, F)$ onto a subset of $\mathfrak{P}(E \times F)$, ordered by inclusion.