Document Zbl 0433.46007

Dilated sets and characterizations of simplexes. (English) Zbl 0433.46007

Invent. Math. 56, 101-108 (1980).

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MSC:

46A55	Convex sets in topological linear spaces; Choquet theory
46A40	Ordered topological linear spaces, vector lattices
52A07	Convex sets in topological vector spaces (aspects of convex geometry)

Keywords:

simplex; dilated set; split face; parallel face; affine function; extension; compact convex set; extreme points

Citations:

Zbl 0225.46014

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Full Text: DOI EuDML

References:

[1]	Alfsen, E. M., On the decomposition of a Choquet simplex into a direct convex sum of complementary faces, Math. Scand., 17, 169-176 (1965) · Zbl 0189.42801
[2]	Alfsen, E. M., Compact convex sets and boundary integrals (1971), Berlin: Springer-Verlag, Berlin · Zbl 0209.42601
[3]	Alfsen, E. M.; Shultz, F. W., Non-commutative spectral theory for affine function spaces on convex sets, Memoirs Amer. Math. Soc., 6, 172 (1976) · Zbl 0337.46013
[4]	Bishop, E.; de Leeuw, K., The representation of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier (Grenoble), 9, 305-331 (1959) · Zbl 0096.08103
[5]	Bishop, E., Phelps, R.R.: The support functionals of a convex set. Proc. Sympos. in Pure Math. 7, Convexity Amer. Math. Soc. 1963 · Zbl 0149.08601
[6]	Briem, E.: A characterization of simplexes by parallel faces. In press (1979) · Zbl 0425.46007
[7]	Effros, E. G., Structure in simplexes II, J. Functional Analysis, 1, 361-391 (1967) · Zbl 0179.17302 · doi:10.1016/0022-1236(67)90008-0
[8]	Effros, E. G., On a class of real Banach spaces, Israel J. Math., 9, 430-458 (1971) · Zbl 0223.46024 · doi:10.1007/BF02771459
[9]	Ellis, A. J., A facial characterization of Choquet simplexes, Bull London Math. Soc., 9, 326-327 (1977) · Zbl 0368.46002 · doi:10.1112/blms/9.3.326
[10]	Hirsberg, B.: A measure theoretic characterization of parallel and split faces and their connections with function spaces and algebras. Aarhus Univ. Various Publications Series No. 16 (1970) · Zbl 0222.46025
[11]	McDonald, J. N., Compact convex sets with the equal support property, Pacific J. Math., 37, 429-443 (1971) · Zbl 0217.16006
[12]	Phelps, R. R., Infinite dimensional compact convex polytopes, Math. Scand., 24, 5-26 (1969) · Zbl 0189.42803
[13]	Rogalski, M., Caractérisation des simplexes par des propriétés portant sur les faces fermées et sur les ensembles compacts de points extrémaux, Math. Scand., 28, 159-181 (1971) · Zbl 0225.46014

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