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Use this tag for questions that specifically address the role of the Hausdorff (T_2) condition, or about the set of Hausdorff topologies, etc. For a topological question with the Hausdorff assumption, just use [gn.general-topology].

9 votes

How do the compact Hausdorff topologies sit in the lattice of all topologies on a set?

In fact there are spaces which are "minimal Hausdorff" -- they have no coarser Hausdorff topology -- but are not compact. It turns out that these spaces are "H-closed" (every open cover has a finite s …