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The Poulsen simplex

Joram LindenstraussGunnar OlsenY. Sternfeld — 1978

Annales de l'institut Fourier

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 2 . The matrices which represent A ( S ) are characterized.

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