Topological spaces containing compact perfect sets and Prohorov spaces (Q1063895)

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.