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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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Quotient of a Hausdorff topological group by a closed subgroup
In fact, an even stronger statement holds: If $G$ is a topological group and $H$ is an (abstract) subgroup, then $G/H$ is Hausdorff if and only if $H$ is closed (cf Bourbaki, General Topology, III.2.5 …