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About: Remote point     Goto   Sponge   NotDistinct   Permalink

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In general topology, a remote point is a point that belongs to the Stone–Čech compactification of a Tychonoff space but that does not belong to the topological closure within of any nowhere dense subset of . Let be the real line with the standard topology. In 1962, Nathan Fine and Leonard Gillman proved that, assuming the continuum hypothesis: There exists a point in that is not in the closure of any discrete subset of ... Their proof works for any Tychonoff space that is separable and not pseudocompact.