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

Lin, Shou

Tsukuba J. Math. 21, No. 3, 809-815 (1997).

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.

Keywords:

compact map; perfect map; \(G_\delta\)-diagonal; closed-map; \(k\)-semistratifiable space; \(\sigma\)-space