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Covering Games and the Banach-Mazur Game: K-tactics

Published online by Cambridge University Press:  20 November 2018

Tomek Bartoszynski ,
Winfried Just  and
Marion Scheepers
Tomek Bartoszynski
Affiliation:
Department of Mathematics Boise State University Boise, Idaho 83725 U.S.A.
Winfried Just
Affiliation:
Department of Mathematics Boise State University Boise, Idaho 83725 U.S.A.
Marion Scheepers
Affiliation:
Department of Mathematics Ohio University Athens, Ohio 45701 U.S.A.
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Abstract

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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.

Keywords

46G0546B0349J5058C2046A1746B2052A41Key words and phrases:Gateaux differentiabilityFréchet differentiabilityweak Hadamard differentiability(not)containing lsub1/subrenormingweaksup*/supKadec propertyconvex functionsnon-compact operators © Canadian Mathematical Society 1993
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 897 - 929
Copyright
Copyright © Canadian Mathematical Society 1993

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