The Banach–Mazur game and domain theory

Abstract

We prove that a player α has a winning strategy in the Banach-Mazur game on a space X if and only if X is F-Y countably π-domain representable. We show that Choquet complete spaces are F-Y countably domain representable. We give an example of a space, which is F-Y countably domain representable, but it is not F-Y π-domain representable.Date: ver.30.