Displaying similar documents to “A Characterization of L Spaces”

Closures of faces of compact convex sets

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.

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...