Topological Games and Alster Spaces

Abstract

AbstractIn 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 byGδsubsets. The results include the following: (1) If TWO has a winning strategy in theMenger game on a regular spaceX, thenXis an Alster space. (2) If TWO has a winning strategy in the Rothberger game on a topological spaceX, then theGδ-topology onXis Lindelöf. (3) The Menger game and the compact-open game are (consistently) not dual.