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

Koumoullis, George

Topology Appl. 21, 59-71 (1985).

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.)

Keywords:

Suslin-Borel set; Čech-analytic set; scattered space; first countable Prokhorov-analytic set; first-countable Prokhorov space; scattered spaces

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