Geodesic
Topological Games and Alster Spaces
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 683-696

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DOI

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.
DOI : 10.4153/CMB-2013-048-5
Mots-clés : 54D20, 54G99, 54A10, topological games, selection principles, Alster spaces, Menger spaces, Rothberger spaces, Menger game, Rothberger game, compact-open game, Gδ -topology 
Aurichi, Leandro F.; Dias, Rodrigo R. Topological Games and Alster Spaces. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 683-696. doi: 10.4153/CMB-2013-048-5
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     title = {Topological {Games} and {Alster} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {683--696},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2013-048-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-048-5/}
}
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