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On coverings of plane convex sets by translates of strips

✍ Scribed by H. Groemer

Publisher
Springer
Year
1981
Tongue
English
Weight
369 KB
Volume
22
Category
Article
ISSN
0001-9054

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πŸ“œ SIMILAR VOLUMES

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Let S be a compact set in the plane. If every three points of S are illuminated dearly by some translate of the compact convex set T, then there is a translate of T which illumines every point of S. Various analogues hold for translates of fiats in R d as well. Mathematics subject classifications (

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 \(F\).