2026/06/26 by Serhii Bardyla, Jaroslav Šupina · 1 voice
Mathematics · #math.GN
For a given Tychonoff space X, a point p∈ β(X)∖ X is called \em remote if p is not in the closure of any nowhere dense subset of X. In this paper, we characterize spaces with remote points in terms of certain topological ultrafilters, measures, and compact-like properties corresponding to the ideal consisting of nowhere dense sets. It is shown that the space of remote points is homeomorphic to a subspace of the Stone space taken over the smallest Boolean algebra containing all open and nowhere dense sets. Also, we show that the space of remote points of \mathbb R is ω-bounded.