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On \(ls\)-Ponomarev systems and \(s\)-images of locally separable metric spaces. (English) Zbl 1168.54013

Summary: We introduce the notion of an \(l\)s-Ponomarev system (\(f,M,X, \{{\mathcal P}_\lambda \}\)), and use this notion to give the necessary and sufficient conditions such that the mapping \(f\) is an \(s\)-mapping (a compact-covering mapping, a sequence-covering mapping, a pseudo-sequence-covering mapping, a sequentially quotient mapping) from a locally separable metric space \(M\) onto a space \(X\). As applications of these results, we systematically get the internal characterizations of certain \(s\)-images of locally separable metric spaces.

MSC:

54E40 Special maps on metric spaces
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54E35 Metric spaces, metrizability
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