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Products of normal spaces with Lašnev spaces. (English) Zbl 0567.54006
In this interesting paper, the author extends some results known for metrizable spaces to Lashnev spaces (that is, to spaces which are closed images of metrizable spaces). Two main results are: Theorem 1. If x is normal, Y is Lashnev and \(X\times Y\) is countably paracompact, then \(X\times Y\) is normal. Theorem 2. If Y is Lashnev and \(X\times Y\) is normal, then \(X\times Y\) is countably paracompact (for metrizable Y, see M. E. Rudin and M. Starbird, Gen. Topology Appl. 5, 235-248 (1975; Zbl 0305.54010)). He also proves, for X normal and countably paracompact and Y Lashnev, that \(X\times Y\) is normal if and only if \(X\times Y\) is countably paracompact, and announces that this result also holds for Y paracompact and \(F_{\sigma}\)-metrizable [see the author’s paper in Quest. Answers Gen. Topology 1, 54-56 (1983; Zbl 0529.54019)].
Reviewer: P.J.Collins

MSC:
54B10 Product spaces in general topology
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54E20 Stratifiable spaces, cosmic spaces, etc.
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