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arXiv · 1306.5463

Topological games and Alster spaces

Leandro F. Aurichi·Rodrigo R. Dias
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Abstract

In this paper we study connections between topological games such as Rothberger, Menger and compact-open, and relate these games to properties involving covers by G_{\delta} subsets. The results include: (1) If Two has a winning strategy in the Menger 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 Lindelof. (3) The Menger game and the compact-open game are (consistently) not dual.

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Leandro F. Aurichi, Rodrigo R. Dias. 2013-06-23. Topological games and Alster spaces. https://doi.org/10.4153/cmb-2013-048-5

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