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On a Corson compact space of Todorčević. (English) Zbl 0618.54021
The relationships among various weak covering properties and between these properties and measure-theoretic properties are fascinating. This is an area where the author has made good contributions. The paper under review is no exception. The author presents a meta-Lindelöf space which is not weak submetacompact \((=\) weakly \(\theta\)-refinable). Such a space was constructed using CH several years ago by the author. The present example is in ZFC. The author also gives a ZFC example of a compact Radon space which is not hereditary weak submetacompact. This answers a question of R. J. Gardner who had constructed an example from CH [Houston J. Math. 13, 37-46 (1987)]. The key idea here is the author’s well-known characterizations of Corson compact and Eberlein compact in tems of the covering properties of \(X^ 2\setminus \Delta\) [Topol. Appl. 17, 287-304 (1984; Zbl 0547.54016)].
Reviewer: S.Davis

MSC:
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54G20 Counterexamples in general topology
54D30 Compactness
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