Remote point (original) (raw)

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.