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\(\pi\)-mappings in \(ls\)-Ponomarev-systems. (English) Zbl 1240.54101

The author characterizes spaces \(X\) which are images of locally separable metric spaces under maps from some class in terms of the existence of various types of covers of \(X\). The characterization is carried out for the class of compact mappings, \(\pi \)-mappings and \(\pi \)-\(s\)-mappings together with their variants which in addition are either sequence-covering, compact-covering, pseudo-sequence-covering or sequentially-quotient.

MSC:

54E40 Special maps on metric spaces
54E99 Topological spaces with richer structures
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