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Strict Separation of Convex Sets

✍ Scribed by V. L. Klee, Jr.

Book ID
121755920
Publisher
American Mathematical Society
Year
1956
Tongue
English
Weight
116 KB
Volume
7
Category
Article
ISSN
0002-9939

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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 \(F\).

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