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On countably paracompact spaces and closed maps. (English) Zbl 0681.54006

Author’s abstract: “Here it is shown that the boundary of \(f^{-1}(y)\) is countably compact when X is \(T_ 1\) and countable paracompact, Y is a q-space and f: \(X\to Y\) is a continuous closed surjection, and applications are given concerning (1) the preservation of countable paracompactness under closed mappings, and (2) the creation of metrizable spaces under closed mappings.”
Reviewer: D.E.Cameron

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54E35 Metric spaces, metrizability
54E99 Topological spaces with richer structures
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