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Touching Convex Sets in the Plane

Published online by Cambridge University Press:  20 November 2018

Meir Katchalski  and
János Pach
Meir Katchalski
Affiliation:
Department of Mathematics, Technion-LLT. Haifa 32000 Israel
János Pach
Affiliation:
Courant Institute, New York University New York, New York 10012 U.S.A. and Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127 1364, Budapest Hungary
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Abstract

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Two subsets of the Euclidean plane touch each other if they have a point in common and there is a straight line separating one from the other.

It is shown that there exists a positive constant c such that if are families of plane convex sets with for some k ≥ 1 and if every touches every then either contains k members having nonempty intersection.

Keywords

52A10convex sets
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 495 - 504
Copyright
Copyright © Canadian Mathematical Society 1994

References

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