论文标题
对Menger属性和拓扑游戏的一些观察
Some observations on the mildly Menger property and topological games
论文作者
论文摘要
在本文中，我们定义了两款新游戏 - 温和的Menger游戏和紧凑型游戏。在零维空间中，Menger游戏等同于Menger游戏，紧凑型游戏等同于紧凑型粘液游戏。给出了一个示例，该示例是一个不确定的空间。我们还引入了一个新游戏，即K-Quasi-Component-Clopen游戏，并证明了该游戏等同于紧凑型粘液游戏。然后我们证明了，如果拓扑空间是许多紧凑型套件的准包装组成的结合，那么两个人在温和的Menger游戏中具有胜利的策略。
In this paper, we defined two new games - the mildly Menger game and the compact-clopen game. In a zero-dimensional space, the Menger game is equivalent to the mildly Menger game and the compact-open game is equivalent to the compact-clopen game. An example is given for a space on which the mildly Menger game is undetermined. Also we introduced a new game namely K-quasi-component-clopen game and proved that this game is equivalent to the compact-clopen game. Then we proved that if a topological space is a union of countably many quasi-components of compact sets, then TWO has a winning strategy in the mildly Menger game.
