Families of convex sets closed under intersections, homotheties and uniting increasing sequences of sets
Marek Lassak (1984)
Fundamenta Mathematicae
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Marek Lassak (1984)
Fundamenta Mathematicae
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Kutateladze, S.S. (2002)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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A. K. Roy (1975)
Annales de l'institut Fourier
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This paper gives necessary and sufficient conditions for the closure of a face in a compact convex set to be again a face. As applications of these results, several theorems scattered in the literature are proved in an economical and uniform manner.
Marek Lassak (1984)
Fundamenta Mathematicae
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Ehrhard Behrends (2000)
Studia Mathematica
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The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads...
Florian, August (1996)
Mathematica Pannonica
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Zippin, M. (2000)
Serdica Mathematical Journal
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∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany). The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1] ...
Nachbin, Leopoldo (1993)
Portugaliae mathematica
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D. K. Thomas (1989)
Publications de l'Institut Mathématique
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