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Abstract

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 the weak Lindelöf number of the $G_\delta $ topology on a compact space. 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_\delta $ sets has a continuum-sized subcollection whose union is $G_\delta $-dense.