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Displaying similar documents to “The space of maximal convex sets”

On Bárány's theorems of Carathéodory and Helly type

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...

Pairs of sets with convex union.

Ryszard Urbanski (1997)

Collectanea Mathematica

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In this paper the notion of convex pairs of convex bounded subsets of a Hausdorff topological vector space is introduced. Criteria of convexity pair are proved.