Topologies on $X$ as points in $2^{\mathcal{P}(X)}$

Jorge L. Bruno, Aisling E. McCluskey

A topology on a nonempty set $X$ specifies a natural subset of $\mathcal{P}(X)$. By identifying $\mathcal{P}(\mathcal{P}(X))$ with the totally disconnected compact Hausdorff space…