Infinite games and chain conditions
Tom 234 / 2016
Fundamenta Mathematicae 234 (2016), 229-239
MSC: Primary 54A25, 91A44; Secondary 54F05, 54G10.
DOI: 10.4064/fm232-3-2016
Opublikowany online: 23 May 2016
Streszczenie
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.