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