The Poulsen simplex
Annales de l'Institut Fourier, Volume 28 (1978) no. 1, pp. 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 2 . The matrices which represent A(S) 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 2 . On caractérise les matrices qui représentent A(S).

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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, Volume 28 (1978) no. 1, pp. 91-114. doi : 10.5802/aif.682. http://archive.numdam.org/articles/10.5802/aif.682/

[1] E.M. Alfsen, Compact convex sets and boundary integrals, Springer-Verlag, 1971. | MR | Zbl

[2] C. Bessaga and A. Pelczynski, Selected topics from infinite dimensional topology, Warsaw, 1975. | Zbl

[3] A. B. Hansen and Y. Sternfeld, On the characterization of the dimension of a compact metric space K by the representing matrices of C(K), Israel. J. of Math., 22 (1975), 148-167. | MR | Zbl

[4] R. Haydon, A new proof that every polish space is the extreme boundary of a simplex, Bull. London Math, Soc., 7 (1975), 97-100. | MR | Zbl

[5] A. Lazar, Spaces of affine continuous functions on simplexes, A.M.S. Trans., 134 (1968), 503-525. | MR | Zbl

[6] A. Lazar, Affine product of simplexes, Math. Scand., 22 (1968), 165-175. | MR | Zbl

[7] A. Lazar and J. Lindenstrauss, Banach spaces whose duals are L1 spaces and their representing matrices. Acta Math., 120 (1971), 165-193. | MR | Zbl

[8] W. Lusky, The Gurari space is unique, Arch. Math., 27 (1976), 627-635. | MR | Zbl

[9] W. Lusky, On separable Lindenstrauss spaces, J. Funct. Anal., 26 (1977), 103-120. | MR | Zbl

[10] E.T. Poulsen, A simplex with dense extreme points, Ann. Inst. Fourier, Grenoble, 11 (1961), 83-87. | Numdam | MR | Zbl

[11] Y. Sternfeld, Characterization of Bauer simplices and some other classes of Choquet simplices by their representing matrices, to appear.

[12] P. Wojtaszczyk, Some remarks on the Gurari space, Studia Math., XLI (1972), 207-210. | MR | Zbl

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