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 Gδ 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 Lindelöf property, every cover by Gδ sets has a continuum-sized subcollection whose union is Gδ-dense.
SPADARO, S.D. (2016). Infinite games and chain conditions. FUNDAMENTA MATHEMATICAE, 234, 229-239.
|Data di pubblicazione:||2016|
|Titolo:||Infinite games and chain conditions|
|Citazione:||SPADARO, S.D. (2016). Infinite games and chain conditions. FUNDAMENTA MATHEMATICAE, 234, 229-239.|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4064/fm232-3-2016|
|Appare nelle tipologie:||1.01 Articolo in rivista|