Judyta Bąk: Domain theory and topological games

Tuesday, March 28, 2017, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Judyta Bąk (University of Silesia)

Title: Domain theory and topological games


Domain is a partially ordered set, in which there was introduced some specific relation. We say that a space is domain representable if it is homeomorphic to a space of maximal elements of some domain. In 2015 W. Fleissner and L. Yengulalp introduced a notion of $\pi$–domain representable space, which is analogous of domain representable. We prove that a player $\alpha$ has a winning strategy in the Banach–Mazur game on a space $X$ if and only if $X$ is countably $\pi$–domain representable. We give an example of countably $\pi$–domain representable space, which is not $\pi$–domain representable.

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