Noncompact simplices
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- by S. Simons
- Trans. Amer. Math. Soc. 149 (1970), 155-161
- DOI: https://doi.org/10.1090/S0002-9947-1970-0259556-X
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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
- 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
- David G. Kendall, Simplexes and vector lattices, J. London Math. Soc. 37 (1962), 365–371. MR 138983, DOI 10.1112/jlms/s1-37.1.365
- Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 149 (1970), 155-161
- MSC: Primary 46.01
- DOI: https://doi.org/10.1090/S0002-9947-1970-0259556-X
- MathSciNet review: 0259556