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

Jafari, Saied

Far East J. Math. Sci. 6, No. 6, 997-1001 (1998).

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

Citations:

Zbl 0503.54031; Zbl 0733.54012; Zbl 1034.54500