The Poulsen simplex
Annales de l'Institut Fourier, Tome 28 (1978) no. 1, p. 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 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 2 . The matrices which represent A(S) are characterized.
@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://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, Tome 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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