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EnglishWe 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 |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| InfiniteGamesandChainConditions.pdf | Documento in Pre-print | Administrator | ||
| InfiniteGamesAndChainConditionsFinale.pdf | Versione Editoriale (PDF) | Administrator |
http://hdl.handle.net/20.500.11769/252410
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