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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.
