## Mapping theorems on $$k$$-semistratifiable spaces.(English)Zbl 1025.54501

Summary: The mapping properties of $$k$$-semistratifiable spaces are discussed. The main results are
(1) A closed-map from a $$k$$-semistratifiable space is a compact-covering map.
(2) An open and compact image of a $$k$$-semistratifiable space is a $$\sigma$$-space.
(3) A perfect inverse image of a $$k$$-semistratifiable space is a $$k$$-semistratifiable space if and only if it has a KG-sequence.

### MSC:

 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54E20 Stratifiable spaces, cosmic spaces, etc. 54E18 $$p$$-spaces, $$M$$-spaces, $$\sigma$$-spaces, etc.
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