The Banach-Mazur Game and Generic Existence of Solutions to Optimization Problems

DOI10.2307/2160141zbMath0794.90089OpenAlexW4256193015MaRDI QIDQ4201629

Kenderov, Petar S., Julian Petrov Revalski

Publication date: 1 September 1993

Full work available at URL: https://doi.org/10.2307/2160141

zbMATH Keywords

Banach-Mazur gamecompletely regular topological spaceexistence of a winning strategy

Mathematics Subject Classification ID

Games involving topology, set theory, or logic (91A44) Programming in abstract spaces (90C48)

Related Items (15)

Topological spaces related to the Banach-Mazur game and the generic well- posedness of optimization problems ⋮ Topological games and optimization problems ⋮ A generic factorization theorem ⋮ Variational principles for maximization problems with lower-semicontinuous goal functions ⋮ Spaces of Minimal Usco and Minimal Cusco Maps as Fréchet Topological Vector Spaces ⋮ Fréchet subspaces of minimal usco and minimal cusco maps ⋮ Variational principles in non-metrizable spaces ⋮ Once again on topological spaces containing a dense completely metrizable subset ⋮ On \(\mathcal T_p\)-locally uniformly rotund norms ⋮ Generic well posedness of supinf problems ⋮ Relations between minimal usco and minimal cusco maps ⋮ Fragmentability of sequences of set-valued mappings with applications to variational principles ⋮ Variational principles and topological games ⋮ The Banach-Mazur game and domain theory ⋮ Strongly Convex Functions, Moreau Envelopes, and the Generic Nature of Convex Functions with Strong Minimizers

Cites Work

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• Borel selectors for upper semi-continuous set-valued maps
• Topological games: on the 50th anniversary of the Banach-Mazur game
• Stratégies gagnantes dans certains jeux topologiques
• Topological spaces with dense subspaces that are homeomorphic to complete metric spaces and the classification of C(K) Banach spaces
• Internal characterization of fragmentable spaces
• Radon‐Nikodým compact spaces and fragmentability
• Topological Spaces That are α-Favorable for a Player with Perfect Information
• Generic well‐posedness of optimization problems in topological spaces

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