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Generalized metric spaces and metrization. (English) Zbl 0794.54034
Hušek, Miroslav (ed.) et al., Recent progress in general topology. Papers from the Prague Toposym 1991, held in Prague, Czechoslovakia, Aug. 19-23, 1991. Amsterdam: North-Holland. 239-274 (1992).
This is a survey (without proofs) of results related to generalized metric spaces and metrization that have been obtained since the author’s previous survey (with proofs) in [Handbook of set-theoretic topology, 423-501 (1984; Zbl 0555.54015)]. The following topics are discussed: symmetrizable spaces, Collins-Roscoe theorem, monotonically normal spaces, Moore spaces, reflection theorems, the strict \(p\)- and \(w \delta\)-space problems, MOBI, stratifiable spaces, Lashnev spaces, \(k\)- networks, and \(\aleph\)-spaces, cosmic spaces, cleavable spaces, normality of products and \(\Sigma\)-spaces. Briefly discussed are the topics: small diagonal, paracompactness of \(X^ 2-\Delta\), Hodel’s vs Mrówka’s metrization numbers, Lashnev decomposition theorems, and certain kinds of bases (e.g., point-countable bases).
For the entire collection see [Zbl 0782.00072].

MSC:
54E35 Metric spaces, metrizability
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