论文标题
拓扑游戏定义的Baire空间类别
Classes of Baire spaces defined by topological games
论文作者
论文摘要
该文章研究了研究拓扑结构（例如寄生虫和半流动组）的操作连续性研究中出现的拓扑游戏。这些游戏是Banach-Mazur游戏的修改。 给定Banach类型的两个玩家游戏$ g（x）$，我们定义$γ^g $ -baire，$γ^g $ -nonMeager和$γ^g $ -spaces。如果第二个玩家在$ g（x）$中没有获胜的策略，则$ x $是$γ^g $ -baire。 $γ^g $ -nonmeager空间和$γ^g $ - 空格的类别在$ g（x）$的修改的帮助下进行了类似的定义。 对于正在考虑的游戏，发现了同等游戏，这有助于研究所得的空间类别之间的关系并确定哪个空间属于这些类别。为此，我们介绍了Banach-Mazur游戏的修改，该游戏与四个玩家。 本文的结果在研究中发现了应用程序的连续性在具有拓扑结构的组中。
The article studies topological games that arise in the study of the continuity of operations in groups with topology, such as paratopological and semitopological groups. These games are modifications of the Banach--Mazur game. Given a two-player game $G(X)$ of the Banach--Mazur type, we define $Γ^G$-Baire, $Γ^G$-nonmeager and $Γ^G$-spaces. A space $X$ is a $Γ^G$-Baire if the second player does not have a winning strategy in $G(X)$. The classes of $Γ^G$-nonmeager spaces and $Γ^G$-spaces are defined similarly, with the help of modifications of the game $G(X)$. For the games under consideration, equivalent games are found, which facilitates studying the relationship between the resulting classes of spaces and determining which spaces belong to these classes. For this purpose, we introduce a modification of the Banach--Mazur game with four players. Results of this paper find application in the study the continuity of operations in groups with topology.
