Topological games and Alster spaces
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 Gδ 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 Gδ-topology on X is Lindelof. (3) The Menger game and the compact-open game are (consistently) not dual.
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