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.