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 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 sets has a continuum-sized subcollection whose union is -dense.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-3-2016,
author = {Santi Spadaro},
title = {Infinite games and chain conditions},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {229-239},
zbl = {06602791},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-3-2016}
}
Santi Spadaro. Infinite games and chain conditions. Fundamenta Mathematicae, Tome 233 (2016) pp. 229-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm232-3-2016/