$Top(X)$ within $\px$ ]{When lattices meet topology: $Top(X)$ within $\px$.}

Jorge L. Bruno, Aisling E. McCluskey

For a non-empty set $X$, the collection $Top(X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can…