Some variations of the Banach-Mazur game

Banach-Mazur game and open mapping theorem

We discuss a variant of the Banach-Mazur game which has applications to topological open mapping and closed graph theorems.

On winning strategies for Banach-Mazur games

We give topological and game theoretic definitions and theorems nec- essary for defining a Banach-Mazur game, and apply these definitions to formalize the game. We then state and prove two theorems which give necessary conditions for existence of winning strategies for players in a Banach-Mazur game.

The Banach--Mazur game and the strong Choquet game in domain theory

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.

The Banach-Mazur compactum is the Alexandroff compactification of a Hilbert cube manifold

We prove that for every $n>2$, the Banach-Mazur compactum Q(n) is the compactification of a Hilbert cube manifold by the Euclidean point. For $n=2$ this result was proved earlier.

A topological group observation on the Banach--Mazur separable quotient problem

The Banach-Mazur problem, which asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient space, has remained unsolved for 85 years, but has been answered in the affirmative for special cases such as reflexive Banach spaces. It is also known that every infinite-dimensional non-normable Fréchet space has an infinite-dimensional separable quotient space, namely $\mathbb{R}^ω$. It is proved in this paper that every infinite-dimensional Fréchet space (including every infinite-dimensional Banach space), indeed every locally convex space which has a subspace whic…

由拓扑博弈定义的Baire空间类

Classes of Baire spaces defined by topological games

该研究围绕带拓扑群的运算连续性问题展开，通过引入四人Banach–Mazur博弈变体，定义了三类由拓扑博弈刻画的Baire相关空间并找到等价博弈，成果可用于拓扑群运算连续性研究。