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On metrizable type (MT-) maps and spaces. (English) Zbl 0953.54017

The authors define paracompact, collectionwise normal, metrizable type (MT) and other types of maps, and prove their properties and relations similar to the classical ones for corresponding properties of spaces. From other results: (Corollary 5.14) A T\(_3\)-space having a \(G_\delta\)-diagonal is metrizable provided it is an MT-preimage of a metrizable space (thus, e.g., there is no MT-map mapping the Sorgenfrey line into a metrizable space – Proposition 4.10).

MSC:

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

Keywords:

metrizable maps
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