A simplex with dense extreme points
Annales de l'Institut Fourier, Volume 11 (1961), p. 83-87

L’article décrit la construction (dans l’espace de Hilbert l 2 ) d’un simplexe (terminologie de Choquet) compact qui est la fermeture de l’ensemble de ses points extrémaux.

@article{AIF_1961__11__83_0,
     author = {Poulsen, Ebbe T.},
     title = {A simplex with dense extreme points},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {11},
     year = {1961},
     pages = {83-87},
     doi = {10.5802/aif.109},
     zbl = {0104.08402},
     mrnumber = {23 \#A1224},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1961__11__83_0}
}
A simplex with dense extreme points. Annales de l'Institut Fourier, Volume 11 (1961) pp. 83-87. doi : 10.5802/aif.109. http://www.numdam.org/item/AIF_1961__11__83_0/

[1] Choquet Gustave, Existence et unicité des représentations intégrales au moyen des points extrémaux dans les cônes convexes. Séminaire Bourbaki (Décembre 1956), 139-01-139-15. | Numdam | Zbl 0121.09204

[2] Klee V. L. Jr., Some new results on smoothness and rotundity in normed linear spaces. To appear.

[3] Krein M. and Milman D., On extreme points of regular convex sets. Studia Math., 9 (1940), 133-138. | JFM 66.0533.01 | MR 3,90a | Zbl 0063.03360

[4] Poulsen Ebbe Thue, Convex sets with dense extreme points. Amer. Math. Monthly, 66 (1959), 577-578. | MR 21 #5882 | Zbl 0104.08401