Infinite games and chain conditions

@article{SantiSpadaro2016,
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 $G_\{δ\}$ 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 $G_\{δ\}$ sets has a continuum-sized subcollection whose union is $G_\{δ\}$-dense.},
author = {Santi Spadaro},
journal = {Fundamenta Mathematicae},
keywords = {chain conditions; selectively ccc; selection principles; weakly lindel"of; topological games; cardinal inequality},
language = {eng},
number = {3},
pages = {229-239},
title = {Infinite games and chain conditions},
url = {http://eudml.org/doc/286469},
volume = {234},
year = {2016},
}

TY - JOUR
AU - Santi Spadaro
TI - Infinite games and chain conditions
JO - Fundamenta Mathematicae
PY - 2016
VL - 234
IS - 3
SP - 229
EP - 239
AB - 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 $G_{δ}$ 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 $G_{δ}$ sets has a continuum-sized subcollection whose union is $G_{δ}$-dense.
LA - eng
KW - chain conditions; selectively ccc; selection principles; weakly lindel"of; topological games; cardinal inequality
UR - http://eudml.org/doc/286469
ER -