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.
Titolo: | Infinite games and chain conditions | |
Autori interni: | ||
Data di pubblicazione: | 2016 | |
Rivista: | ||
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 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. | |
Handle: | http://hdl.handle.net/20.500.11769/252410 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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