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Topological spaces containing compact perfect sets and Prohorov spaces. (English) Zbl 0574.54041

Generalizing the known facts for Borel and Suslin subsets of complete metric spaces, the author proves that if X is either Čech-analytic or first countable Prokhorov-analytic, then X is \(\sigma\)-scattered or contains a compact perfect set. The assertion implies e.g. that every first-countable Prokhorov space is a Baire space, that the Sorgenfrey line is not Prokhorov (neither Prokhorov-analytic). First-countable scattered and \(\sigma\)-scattered spaces are then characterized by means of the Prokhorov property.
Reviewer: M.Hušek

MSC:

54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
54E52 Baire category, Baire spaces
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
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