A simplex with dense extreme points

Ebbe T. Poulsen

Displaying similar documents to “A simplex with dense extreme points”

The Poulsen simplex

Joram Lindenstrauss, Gunnar Olsen, Y. Sternfeld (1978)

Annales de l'institut Fourier

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It is proved that there is a unique metrizable simplex $S$ whose extreme points are dense. This simplex is homogeneous in the sense that for every 2 affinely homeomorphic faces $F_{1}$ and $F_{2}$ there is an automorphism of $S$ which maps $F_{1}$ onto $F_{2}$ . Every metrizable simplex is affinely homeomorphic to a face of $S$ . The set of extreme points of $S$ is homeomorphic to the Hilbert space $ℓ_{2}$ . The matrices which represent $A (S)$ are characterized.

The Space of Differences of Convex Functions on [0, 1]

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] ...

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.