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A Helly type Theorem for Convex Sets

Published online by Cambridge University Press:  20 November 2018

Meir Katchalski
Meir Katchalski*
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1
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Abstract

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A ray in Euclidean n-dimensional space Rn is a set of the form {a + λb: λ≥ 0 } where a and b are fixed points in Rn and b≠0.

The subject of this paper is a Helly type theorem for convex sets in Rn.

If is a finite family of at least 2n convex sets in Rn and if theintersection of any 2n members of contains a ray then containsa ray.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 1 , 01 March 1978 , pp. 121 - 123
Copyright
Copyright © Canadian Mathematical Society 1978

References

[1] Danzer, L., Gr, B.ûnbaum and Klee, V., Helly's theorem and its relatives, Proceedings of Symposia in Pure Mathematics, Vol. 7, Convexity, Amer. Math. Soc. (1962), 101-180.Google Scholar
[2] De, R. Santis, A generalization of Helley's theorem, Proc. Amer. Math. Soc. 8 (1957), 336-340.Google Scholar
[3] Grünbaum, B., The dimension of intersections of convex sets, Pacific J. Math. 12 (1962), 197-202.Google Scholar
[4] Grünbaum, B., Convex Polytopes, Interscience, London/New York/Sydney, 1967.Google Scholar
[5] Katchalski, M., The dimensions of intersections of convex ‘sets, Israel J. Math. 10 (1971), 465-470.Google Scholar