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On separation properties
of finite dimensional compact convex sets


Authors: João F. Queiró and Eduardo M. Sà
Journal: Proc. Amer. Math. Soc. 124 (1996), 259-264
MSC (1991): Primary 52A20
DOI: https://doi.org/10.1090/S0002-9939-96-03380-1
MathSciNet review: 1327040
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Abstract | References | Similar Articles | Additional Information

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

  • 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: https://doi.org/10.1090/S0002-9939-96-03380-1
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
Article copyright: © Copyright 1996 American Mathematical Society

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