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Valuations on Convex Sets of Oriented Hyperplanes

✍ Scribed by John Gates; Daniel Hug; Rolf Schneider


Publisher
Springer
Year
2004
Tongue
English
Weight
193 KB
Volume
33
Category
Article
ISSN
0179-5376

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On Separation of Plane Convex Sets
✍ Eduardo Rivera-Campo; JenΓΆ TΓΆrΓΆcsik πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 77 KB

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 \(F\).