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A note on sober pre-regular spaces. (English) Zbl 1038.54505

Summary: G. J. Wang [Acta Math. Sin. 24, 55–63 (1981; Zbl 0503.54031)] and M. Ganster [Glas. Mat., III. Ser. 25(45), No. 1, 195–201 (1990; Zbl 0733.54012)] quite independently introduced the notions of \(P_\Sigma\) and strongly \(s\)-regular spaces, respectively. M. Khan, T. Noiri and B. Ahmad [Mat. Vesn. 48, No. 3–4, 87–93 (1996; Zbl 1034.54500)] showed that these two notions are equivalent. The object of this paper is so investigate sober preregularity which implies strongly \(s\)-regularity.

MSC:

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