Infinite games and chain conditions
General Topology
2015-07-09 v1
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 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 sets has a continuum-sized subcollection whose union is -dense.
Cite
@article{arxiv.1507.02134,
title = {Infinite games and chain conditions},
author = {Santi Spadaro},
journal= {arXiv preprint arXiv:1507.02134},
year = {2015}
}