A universal coregular countable second-countable space

2020/03/13 by Banakh, Taras, Stelmakh, Yaryna
#37B05 #51H10 #54F65 #54G15 #57N20 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2003.06293

Abstract

A Hausdorff topological space X is called superconnected (resp. coregular) if for any nonempty open sets U₁,… U_n⊆ X, the intersection of their closures U₁∩…∩ U_n is not empty (resp. the complement X∖ ( U₁∩…∩ U_n) is a regular topological space). A canonical example of a coregular superconnected space is the projective space \mathbb Q\mathsf P^∞ of the topological vector space \mathbb Q^

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