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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Banach-Mazur game and generic existence of solutions to optimization problems


Authors: P. S. Kenderov and J. P. Revalski
Journal: Proc. Amer. Math. Soc. 118 (1993), 911-917
MSC: Primary 49J27; Secondary 90C48, 90D44
MathSciNet review: 1137224
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Abstract: The existence of a winning strategy in the well-known Banach-Mazur game in a completely regular topological space $ X$ is proved to be equivalent to the generic existence of solutions of optimization problems generated by continuous functions in $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1137224-0
PII: S 0002-9939(1993)1137224-0
Keywords: Banach-Mazur game, winning strategy, generic, optimization problems
Article copyright: © Copyright 1993 American Mathematical Society