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Games, hereditarily Baire hyperspaces and Mengerness at infinity
- Speaker(s)
- Mikołaj Krupski
- Affiliation
- University of Warsaw
- Date
- Dec. 19, 2018, 4:15 p.m.
- Room
- room 5050
- Seminar
- Topology and Set Theory Seminar
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.
In my talk I will focus on the following problem: Let X be a separable metric space. When the hyperspace K(X) of all nonempty compact subsets of X endowed with the Hausdorff metric is hereditarily Baire?
A satisfactory answer to the above question was recently given by Gartside, Medini and Zdomskyy who observed its connection with a property of the remainder of some (any) compactification of X (the Menger property).
Using topological games, I will give an alternative, simple proof of their theorem. In fact, I will show that it easily reduces to a certain (simple) result of Telgarsky.
