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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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Why the name 'separable' space?
Well "séparer" means just "disjoin", "split up" etc. There are few meanings for "séparation" in french. For exemple "séparer par des fonctions". If you have a space $X$ and a set of functions ${\cal F …