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Multiplier rules and the separation of convex sets

✍ Scribed by B. H. Pourciau

Publisher
Springer
Year
1983
Tongue
English
Weight
594 KB
Volume
40
Category
Article
ISSN
0022-3239

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On Separation of Plane Convex Sets
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We show that in any family \(F\) of \(n \geqslant 5\) convex sets in the plane with pairwise disjoint relative interiors, there are two sets \(A\) and \(B\) such that every line that separates them, separates either \(A\) or \(B\) from at least \((n+28) / 30\) sets in \(F\).