Geodesic
Covering Games and the Banach-Mazur Game: K-tactics
Canadian journal of mathematics, Tome 45 (1993) no. 5, pp. 897-929

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Given a free ideal J of subsets of a set X, we consider games where player ONE plays an increasing sequence of elements of the σ-completion of J, and player TWO tries to cover the union of this sequence by playing one set at a time from J. We describe various conditions under which player TWO has a winning strategy that uses only information about the most recent k moves of ONE, and apply some of these results to the Banach-Mazurgame.
DOI : 10.4153/CJM-1993-051-4
Mots-clés : 46G05, 46B03, 49J50, 58C20, 46A17, 46B20, 52A41, Key words and phrases:, Gateaux differentiability, Fréchet differentiability, weak Hadamard differentiability, (not)containing l, sub, 1, /sub, renorming, weak, sup, *, /sup, Kadec property, convex functions, non-compact operators © Canadian Mathematical Society 1993 
Bartoszynski, Tomek; Just, Winfried; Scheepers, Marion. Covering Games and the Banach-Mazur Game: K-tactics. Canadian journal of mathematics, Tome 45 (1993) no. 5, pp. 897-929. doi: 10.4153/CJM-1993-051-4
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