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Cross-posted from Math.SE: https://math.stackexchange.com/questions/4948421/. I'm interested in comparing $k_1$-spaces, spaces whose topologies are witnessed by their compact subspaces, and $k_3$-...

We know that all closed subsets of a compact topological space $(X,\tau)$ are compact. If we add the Hausdorff condition on the topology $\tau$ we can see the equivalence of these conditions on a ...