## 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

### Citations:

Zbl 0503.54031; Zbl 0733.54012; Zbl 1034.54500