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A note on intersections of simplices. (Sur certaines intersections de simplexes.) (English. French summary) Zbl 1227.46011

Summary: We provide a corrected proof of D. A. Edwards [ibid. 103, 225–240 (1975; Zbl 0346.46002), Théorème 9], stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.

MSC:

46A55 Convex sets in topological linear spaces; Choquet theory
52A07 Convex sets in topological vector spaces (aspects of convex geometry)

Citations:

Zbl 0346.46002
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References:

[1] A. J. Lazar & J. Lindenstrauss -“Banach spaces whose duals are L 1 spaces and their representing matrices”, Acta Math. 126 (1971), p. 165-193. · Zbl 0209.43201
[2] J. Lindenstrauss, G. H. Olsen & Y. Sternfeld -“The Poulsen simplex”, Ann. Inst. Fourier (Grenoble) 28 (1978), p. 91-114. · Zbl 0363.46006
[3] Y. Sternfeld -“Characterization of Bauer simplices and some other classes of Choquet simplices by their representing matrices”, in Notes in Banach spaces, Univ. Texas Press, 1980, p. 306-358. · Zbl 0556.46006
[4] BULLETIN DE LA SOCIÉTÉ MATHÉMATIQUE DE FRANCE
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