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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Sem. Topologia i T. Mnogości


Hereditarily Baire hyperspaces, filters and spaces of measures

Prelegent: Mikołaj Krupski

2019-10-09 16:15

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.