arXiv:1306.5463 Abstract | arXiv Analytics

arXiv:1306.5463 [math.GN]Abstract References Reviews Resources

Topological games and Alster spaces

Published 2013-06-23, updated 2013-06-27Version 2

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.

Comments: 13 pages; submitted

Categories: math.GN

Subjects: 54D20, 54G99, 54A10

Keywords: alster space, topological games, menger game, winning strategy, study connections

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