Geodesic
Applications of limited information strategies in Menger's game
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 2, pp. 225-239.

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As shown by Telgársky 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.
DOI : 10.14712/1213-7243.2015.201
Classification : 03E35, 54D20, 54D45, 91A44
Keywords: Menger property; Menger game; $\sigma$-compact spaces; limited information strategies 
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Clontz, Steven. Applications of limited information strategies in Menger's game. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 2, pp. 225-239. doi : 10.14712/1213-7243.2015.201. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.201/

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