Judyta Bąk

# Judyta Bąk: Domain theory and topological games

Tuesday, March 28, 2017 17:15

Room: D1-215

Speaker:
Judyta Bąk

Title: Domain theory and topological games

Abstract. 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.