zbMATH — the first resource for mathematics

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].

54E35 Metric spaces, metrizability