## On $$P_\Sigma$$ and weakly-$$P_\Sigma$$ spaces.(English)Zbl 1034.54500

Several weak forms of regularity, in particular $$P_\Sigma$$-spaces, weakly $$P_\Sigma$$-spaces and strongly $$s$$-regular spaces, are studied. It is shown that the class of $$P_\Sigma$$-spaces coincides with the class of strongly $$s$$-regular spaces. Preservation of these properties under different kinds of mappings is also considered.

### MSC:

 54D10 Lower separation axioms ($$T_0$$–$$T_3$$, etc.) 54B05 Subspaces in general topology 54C08 Weak and generalized continuity
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