Hereditarily Baire hyperspaces, filters and spaces of measures - part 2

Speaker(s)

Mikołaj Krupski

Affiliation

University of Warsaw

Date

Oct. 16, 2019, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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This part does not depend on the material presented under the same title during the first part of the talk. A topological space X is Baire if the intersection of a countable family of open dense sets in X is dense. We say that X is hereditarily Baire if every closed subspace of X is Baire. It was observed by the speaker that hereditary Baireness of the hyperspace of all nonempty compact subsets of a separable metrizable space X can be conveniently described in terms of a certain topological game on X. I will show how we can apply this result to study hereditary Baireness of two types of objects: hyperspaces over filters on natural numbers and spaces P(X) of Borel Radon probability measures on a separable metrizable space X.

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