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 [10.4064/fm232-3-2016].

Infinite games and chain conditions

SPADARO, SANTI DOMENICO
2016

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.
https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/all/234/3/91491/infinite-games-and-chain-conditions
SPADARO, S.D. (2016). Infinite games and chain conditions. FUNDAMENTA MATHEMATICAE, 234, 229-239 [10.4064/fm232-3-2016].
File in questo prodotto:
File Dimensione Formato  
InfiniteGamesandChainConditions.pdf

accesso aperto

Tipologia: Pre-print
Dimensione 277.41 kB
Formato Adobe PDF
277.41 kB Adobe PDF Visualizza/Apri
InfiniteGamesAndChainConditionsFinale.pdf

Solo gestori archvio

Tipologia: Versione Editoriale
Dimensione 289.22 kB
Formato Adobe PDF
289.22 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/480970
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact