Example 2

For each partition $\varpi$ of a set E, let $\tilde{\varpi}$ be the graph of the equivalence relation defined by $\varpi$ on E. The mapping $\varpi \to \tilde{\varpi}$ is an isomorphism of the set $\mathfrak{L}$ of partitions of E, ordered by the relation "$\varpi$ is finer than $\varpi'$" between $\varpi$ and $\varpi'$ (no. 1, Example 4) onto a subset of $\mathfrak{P}(E \times E)$, ordered by inclusion.