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Topological Games and Alster Spaces

Published online by Cambridge University Press:  20 November 2018

Leandro F. Aurichi  and
Rodrigo R. Dias
Leandro F. Aurichi
Affiliation:
Instituto de Ciências Matemáticas e de Computaçao, Universidade de São Paulo, Caixa Postal 668, Sāo Carlos, SP, 13560-970, Brazil e-mail: aurichi@icmc.usp.br
Rodrigo R. Dias
Affiliation:
Instituto de Matemática e Estatística, Universidade de Paulo, Caixa Postal 66281, Paulo, SP, 05315- 970, Brazil e-mail: roque@ime.usp.br
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Abstract

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In this paper we study connections between topological games such as Rothberger, Menger, and compact-open games, and we relate these games to properties involving covers by ${{G}_{\delta }}$ subsets. The results include the following: (1) If TWO has a winning strategy in theMenger game on a regular space $X$, then $X$ is an Alster space. (2) If TWO has a winning strategy in the Rothberger game on a topological space $X$, then the ${{G}_{\delta }}$-topology on $X$ is Lindelöf. (3) The Menger game and the compact-open game are (consistently) not dual.

Keywords

54D2054G9954A10topological gamesselection principlesAlster spacesMenger spacesRothberger spacesMenger gameRothberger gamecompact-open gameGδ-topology
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 4 , 01 December 2014 , pp. 683 - 696
Copyright
Copyright © Canadian Mathematical Society 2014

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