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Notes on \(cfp\)-covers. (English) Zbl 1100.54021

Summary: The main purpose of this paper is to establish general conditions under which \(T_2\)-spaces are compact-covering images of metric spaces by using the concept of \(cfp\)-covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of \(g\)-metrizable spaces by compact-covering \(\sigma \)-maps and \(mssc\)-maps.

MSC:

54E40 Special maps on metric spaces
54E18 \(p\)-spaces, \(M\)-spaces, \(\sigma\)-spaces, etc.
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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