The Poulsen simplex
Annales de l'Institut Fourier, Tome 28 (1978) no. 1, pp. 91-114.

On démontre ici qu’il existe un seul simplexe métrisable S dont les points extrémaux sont denses. Ce simplexe est homogène au sens que pour tout couple de face F 1 , F 2 affinement homéomorphes, il existe un automorphisme de S qui transforme F 1 en F 2 . Tout simplexe métrisable est affinement homéomorphe à une face de S. L’ensemble des points extrémaux de S est homéomorphe à l’espace de Hilbert ℓ 2 . On caractérise les matrices qui représentent A(S).

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.

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     title = {The {Poulsen} simplex},
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Lindenstrauss, Joram; Olsen, Gunnar; Sternfeld, Y. The Poulsen simplex. Annales de l'Institut Fourier, Tome 28 (1978) no. 1, pp. 91-114. doi : 10.5802/aif.682. http://archive.numdam.org/articles/10.5802/aif.682/

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