Noncompact simplices
Author:
S. Simons
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
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Abstract | References | Similar Articles | Additional Information
Abstract: A bounded, but not necessarily closed, (Choquet) simplex in 
with nonempty interior is the intersection of 
half-spaces. There is no bounded simplex with nonempty interior in an infinite dimensional Hausdorff real linear topological space.
- [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 138983, https://doi.org/10.1112/jlms/s1-37.1.365
- [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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1970-0259556-X
Keywords:
Choquet simplex,
linearly compact,
abstract L-space
Article copyright:
© Copyright 1970
American Mathematical Society
