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On strongly s-regular spaces. (English) Zbl 0733.54012

Strongly s-regular spaces are introduced and studied. A topological space X is said to be strongly s-regular if for every closed subset \(A\subset X\) and \(x\in X\setminus A\) there exists a regular closed subset F \((F=cl(int F))\) with \(x\in F\) and \(F\cap A=\emptyset\). Strong s- regularity is open-hereditary and productive. Among Hausdorff spaces strong s-regularity is independent both of semiregularity and of almost regularity.

MSC:

54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54G20 Counterexamples in general topology
54B10 Product spaces in general topology
54B05 Subspaces in general topology
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