无限对策与链条件

摘要：

我们将无限两人对策的理论应用于两个著名的拓扑学问题：关于紧空间的$G_δ$覆盖的Suslin问题和Arhangel'skii问题.更具体地说，我们证明了以下两个结果的特殊情况：1）每个线性序拓扑空间满足博弈论版本的可数链条件是可分的，2）在每个紧空间满足博弈论版本的弱Lindelöf性质，每个覆盖由$G_δ$集有一个连续大小的子集，其联合是$G_δ$ -稠密。

英文摘要：

We apply the theory of infinite two-person games to two well-known problems in topology: Suslin's Problem and Arhangel'skii's problem on $G_δ$ covers of compact spaces. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable and 2) in every compact space satisfying the game-theoretic version of the weak Lindelöf property, every cover by $G_δ$ sets has a continuum-sized subcollection whose union is $G_δ$-dense.

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