On \(F_\sigma\text{-}\delta\)-normality and hereditary \(\delta\)-normality
type: Item
instance of: scholarly article
title: On \(F_\sigma\text{-}\delta\)-normality and hereditary \(\delta\)-normality
zbMATH Open document ID: 0935.54019
DOI: 10.1016/S0166-8641(97)00205-8
published in: Topology and its Applications
publication date: 2000-05-03T00:00:00Z
review text: By \textit{J. Mack} [Trans. Am. Math. Soc. 148, 265-272 (1970; Zbl 0209.26904)] a topological space \(X\) is called \(\delta\)-normal if one can separate (by open sets) each closed set and each disjoint regularly closed \(G_\delta\)-set. It is shown that if \(X\times Y\) is hereditarily (or \(F_\sigma\)-hereditarily) \(\delta\)-normal, then either \(X\) is perfectly normal (or normal and countably paracompact, resp.) or all countable subsets of \(Y\) are closed. The results are applied to \(C_p(X)\): every \(F_\sigma\)-hereditarily \(\delta\)-normal \(C_p(X)\) is normal, and every hereditarily \(\delta\)-normal \(C_p(X)\) is perfectly normal.
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 1307889
zbMATH Keywords: \(C_p(X)\)
author: Anatoli P. Kombarov
reviewed by: M. Hušek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1307889