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