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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
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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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