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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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