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On Certain Intersection Properties ofConvex Sets

Published online by Cambridge University Press:  20 November 2018

V. L. Klee Jr.
V. L. Klee Jr.*
Affiliation:
University of Virginia
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A collection of n + 1 convex subsets of a Euclidean space E will be called an n-set in E provided each n of the sets have a common interior point although the intersection of all n + 1 interiors is empty. It is well-known that if {C0,C1} is a 1-set, then C0 and C1 can be separated by a hyperplane.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 272 - 275
Copyright
Copyright © Canadian Mathematical Society 1951

References

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[2] Horn, Alfred, Some generalizations of Helly's theorem on convex sets, Bull. Amer. Math. Soc, vol. 55 (1949), 923–929.Google Scholar
[3] Klee, V. L., Jr., Convex sets in linear spaces, Dissertation (University of Virginia, 1949).Google Scholar
[4] Kakutani, Shizuo, Ein Beweis des Satzes von M. Eidelheit uber konvexe Mengen, Proc. Imp. Acad., Tokyo, vol. 13 (1937), 93–94.Google Scholar
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