Judyta Bąk

Judyta Bąk: Domain theory and topological games

Tuesday, March 28, 2017 17:15

Room: D1-215

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.