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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Noncompact simplices

Author: S. Simons
Journal: Trans. Amer. Math. Soc. 149 (1970), 155-161
MSC: Primary 46.01
MathSciNet review: 0259556
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Abstract: A bounded, but not necessarily closed, (Choquet) simplex in $ {R^n}$ with nonempty interior is the intersection of $ n + 1$ half-spaces. There is no bounded simplex with nonempty interior in an infinite dimensional Hausdorff real linear topological space.

References [Enhancements On Off] (What's this?)

  • [1] Gustave Choquet, Existence et unicité des représentations intégrales au moyen des points extrémaux dans les cônes convexes, Séminaire Bourbaki, Vol. 4, Soc. Math. France, Paris, 1995, pp. Exp. No. 139, 33–47 (French). MR 1610937
  • [2] David G. Kendall, Simplexes and vector lattices, J. London Math. Soc. 37 (1962), 365–371. MR 0138983
  • [3] Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
  • [4] Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1966. MR 0193469

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Keywords: Choquet simplex, linearly compact, abstract L-space
Article copyright: © Copyright 1970 American Mathematical Society