  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 $G_\delta$ 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
Lindel\"of property, every cover by $G_\delta$ sets has a continuum-sized
subcollection whose union is $G_\delta$-dense.
