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On separation properties of finite dimensional compact convex sets
Author(s):
João
F.
Queiró;
Eduardo
M.
Sà
Journal:
Proc. Amer. Math. Soc.
124
(1996),
259-264.
MSC (1991):
Primary 52A20
MathSciNet review:
1327040
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Abstract:
In a real finite-dimensional vector space, we study families of sets such that every compact convex set in the space is the intersection of all members of the family that contains it.
References:
- 1
- V.L. Klee, Extremal Structure of Convex Sets II, Math. Z. 69(1958), 90--104 MR 19:1065b
- 2
- S.R. Lay, On Separation by Spherical Surfaces, Amer. Math. Monthly 78(1971), 1112--1113 MR 45:9248
- 3
- S.R. Lay, Separation by Cylindrical Surfaces, Proc. Amer. Math. Soc. 36(1972), 224--228 MR 46:9865
- 4
- S.R. Lay, Separating two Compact Sets by a Parallelotope, Proc. Amer. Math. Soc. 79(1980), 279--284 MR 81d:52005
- 5
- R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton 1970 MR 43:445
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Additional Information:
João
F.
Queiró
Affiliation:
Departamento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal
Email:
jfqueiro@gemini.ci.uc.pt
Eduardo
M.
Sà
Affiliation:
Departamento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal
DOI:
10.1090/S0002-9939-96-03380-1
PII:
S 0002-9939(96)03380-1
Received by editor(s):
April 20, 1992
Additional Notes:
The authors were partially supported by Instituto Nacional de Investigação Científica and Junta Nacional de Investigação Científica e Tecnológica
Communicated by:
Dale Alspach
Copyright of article:
Copyright
1996,
American Mathematical Society
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