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Separability of convex sets and the concept of convexity on the surface of a convex body

✍ Scribed by A. G. Netrebin


Publisher
SP MAIK Nauka/Interperiodica
Year
1980
Tongue
English
Weight
508 KB
Volume
27
Category
Article
ISSN
0001-4346

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πŸ“œ SIMILAR VOLUMES


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 \(F\).

A three-point convexity property and the
✍ Karsten Juul πŸ“‚ Article πŸ“… 1977 πŸ› Springer 🌐 English βš– 478 KB

In his paper [3], F.A.Valentine has defined a three-point property Pa. The first part of that paper contains results valid in n-space. In the second part is specialized to the plane, and among other things it is proved that a set is the union of two convex sets if it has the property P3 and there is