Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an old question of Bell, Ginsburg and Woods regarding the cardinality of weakly Lindel¨of first-countable regular spaces and answer a question recently asked by Babinkostova, Pansera and Scheepers. In the second part of the paper we study a game-theoretic version of cellularity, a special case of which has been introduced by Aurichi. We obtain a game-theoretic proof of Shapirovskii’s bound for the number of regular open sets in an (almost) regular space and give a partial answer to a natural question about the productivity of a game strengthening of the countable chain condition that was introduced by Aurichi. As a final application of our results we prove that the Hajnal-Juh´asz bound for the cardinalityof a first-countable ccc Hausdorff space is true for almost regular (non-Hausdorff) spaces

BELLA, A., SPADARO, S.D. (2015). Infinite games and cardinal properties of topological spaces. HOUSTON JOURNAL OF MATHEMATICS, 41(3), 1063-1077.

Infinite games and cardinal properties of topological spaces

SPADARO, SANTI DOMENICO
2015-01-01

Abstract

Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an old question of Bell, Ginsburg and Woods regarding the cardinality of weakly Lindel¨of first-countable regular spaces and answer a question recently asked by Babinkostova, Pansera and Scheepers. In the second part of the paper we study a game-theoretic version of cellularity, a special case of which has been introduced by Aurichi. We obtain a game-theoretic proof of Shapirovskii’s bound for the number of regular open sets in an (almost) regular space and give a partial answer to a natural question about the productivity of a game strengthening of the countable chain condition that was introduced by Aurichi. As a final application of our results we prove that the Hajnal-Juh´asz bound for the cardinalityof a first-countable ccc Hausdorff space is true for almost regular (non-Hausdorff) spaces
2015
BELLA, A., SPADARO, S.D. (2015). Infinite games and cardinal properties of topological spaces. HOUSTON JOURNAL OF MATHEMATICS, 41(3), 1063-1077.
File in questo prodotto:
File Dimensione Formato  
Infinite games and cardinal properties of topological spaces.pdf

accesso aperto

Tipologia: Pre-print
Dimensione 192.39 kB
Formato Adobe PDF
192.39 kB Adobe PDF Visualizza/Apri

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: https://hdl.handle.net/10447/480950
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact