English

Topological games and Alster spaces

General Topology 2019-08-15 v2

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.

Keywords

Cite

@article{arxiv.1306.5463,
  title  = {Topological games and Alster spaces},
  author = {Leandro F. Aurichi and Rodrigo R. Dias},
  journal= {arXiv preprint arXiv:1306.5463},
  year   = {2019}
}

Comments

13 pages; submitted

R2 v1 2026-06-22T00:38:52.576Z