## Steven ClontzApplications of limited information strategies in Menger's game

Comment.Math.Univ.Carolin. 58,2 (2017) 225-239.

Abstract:As shown by Telg\'arsky and Scheepers, winning strategies in the Menger game characterize $$\sigma$$-compactness amongst metrizable spaces. This is improved by showing that winning Markov strategies in the Menger game characterize $$\sigma$$-compactness amongst regular spaces, and that winning strategies may be improved to winning Markov strategies in second-countable spaces. An investigation of $$2$$-Markov strategies introduces a new topological property between $$\sigma$$-compact and Menger spaces.

Keywords: Menger property; Menger game; $$\sigma$$-compact spaces; limited information strategies

DOI: DOI 10.14712/1213-7243.2015.201
AMS Subject Classification: 03E35 54D20 54D45 91A44

PDF