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

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 ${\ell }_{2}$. The matrices which represent $A\left(S\right)$ are characterized.

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 ${\ell }_{2}$. On caractérise les matrices qui représentent $A\left(S\right)$.

@article{AIF_1978__28_1_91_0,
author = {Lindenstrauss, Joram and Olsen, Gunnar and Sternfeld, Y.},
title = {The Poulsen simplex},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Louis-Jean},
address = {Gap},
volume = {28},
number = {1},
year = {1978},
pages = {91-114},
doi = {10.5802/aif.682},
zbl = {0363.46006},
mrnumber = {80b:46019a},
language = {en},
url = {http://www.numdam.org/item/AIF_1978__28_1_91_0}
}

Lindenstrauss, Joram; Olsen, Gunnar; Sternfeld, Y. The Poulsen simplex. Annales de l'Institut Fourier, Volume 28 (1978) no. 1, pp. 91-114. doi : 10.5802/aif.682. http://www.numdam.org/item/AIF_1978__28_1_91_0/

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