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Topological games and optimization problems

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  26 February 2010

Gabriel Debs  and
Jean Saint Raymond
Gabriel Debs
Affiliation:
Equipe d'Analyse, Université Paris 6, 4, Place Jussieu, 75252 Paris Cedex 05, France
Jean Saint Raymond
Affiliation:
Equipe d'Analyse, Université Paris 6, 4, Place Jussieu, 75252 Paris Cedex 05, France
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Extract

Let X be a completely regular space, and Cb(X) the space of all bounded continuous real valued functions on X equipped with the metric associated to the uniform norm. For f∈Cb(X) and γ∈¡ we use the following standard notations: inf(f) = infx∈Xf(x) and {f<γ} = {x∈X:f(x)<γ}

MSC classification

Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Mathematika , Volume 41 , Issue 1 , June 1994 , pp. 117 - 132
Copyright
Copyright © University College London 1994

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References

1.Choquet, G.. Lectures on Analysis (Benjamin, New York, 1969).Google Scholar
2.Coban, M. M., Kenderov, P. S. and Revalski, J. P.. Generic well-posedness of optimization problems in topological spaces. Mathematika, 36 (1989), 301–304.CrossRefGoogle Scholar
3.Debs, G.. Espaces hereditairement de Baire. Fund. Math., 129 (1988), 196–206.CrossRefGoogle Scholar
4.Kenderov, P. S. and Revalski, J. P.. The Banach-Mazur game and generic existence of solutions to optimization problems. Proc. Amer. Math. Soc, 118 (1993), 911–917.CrossRefGoogle Scholar
5.Raymond, J. Saint. Jeux topologiques et espaces de Namioka. Proc. Amer. Math. Soc. 87 (1983), 499–504.CrossRefGoogle Scholar
6.Stegall, Ch.. Topological spaces with dense subspaces that are homeomorphic to complete metric space and the classification of C{K) Banach spaces. Mathematika, 34 (1987), 101–107.CrossRefGoogle Scholar
7.Telgarski, R.. Topological games: On the 50-th anniversary of the Banach-Mazur game. Rocky Mount. J. Math., 17 (1987), 227–276.Google Scholar