On \(\pi\)-\(s\)-images of metric spaces. (English) Zbl 1082.54023

Let \((X, d)\) be a metric space. A map \(f:(X, d)\to Y\) is called a \(\pi\)-map if \(d(f^{-1}(y), M-f^{-1}(U))>0\) for each \(y\in Y\) and its open neighborhood \(U\) in \(Y\). In 1965, R. W. Heath proved that a space is developable if and only if it is an image of a metric space under an open and \(\pi\)-mapping. In this paper the images of metric spaces under compact-covering and \(\pi\)-\(s\)-mappings, sequence-covering and \(\pi\)-\(s\)-mappings are characterized, respectively.
Reviewer: Shou Lin (Fujian)


54E99 Topological spaces with richer structures
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54E35 Metric spaces, metrizability
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