On \(P_\Sigma\) and weakly-\(P_\Sigma\) spaces. (English) Zbl 1034.54500

Several weak forms of regularity, in particular \(P_\Sigma\)-spaces, weakly \(P_\Sigma\)-spaces and strongly \(s\)-regular spaces, are studied. It is shown that the class of \(P_\Sigma\)-spaces coincides with the class of strongly \(s\)-regular spaces. Preservation of these properties under different kinds of mappings is also considered.


54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54B05 Subspaces in general topology
54C08 Weak and generalized continuity
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