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The dimension of intersections of convex sets II

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Abstract

The subject of this paper is a Helly type theorem which solves the following problem: Find the smallest number β= β(j,k,n) having the following property: IfG is any finite family ofβ + 1 convex sets in Euclideann-space and if the intersection of everyβ members ofG is at leastk-dimensional, then the intersection of all members ofG is at leastj-dimensional.

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References

  1. L. Danzer, B. Grünbaum and V. Klee,Helley’s theorem and its relatives, Proceedings of Symposia in Pure Mathematics, Vol. 7,Convexity. Amer. Math. Soc. (1962), 101–180.

  2. B.Grünbaum,The dimension of intersections of convex sets. Pacific J. Math.12 (1962), 197–202.

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  3. M. Katchalski,The dimension of intersections of convex sets, Israel J. Math.10 (1971), 465–470.

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Authors and Affiliations

  1. The University of Alberta, Edmonton, Alberta, Canada

    Meir Katchalski

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  1. Meir Katchalski
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Katchalski, M. The dimension of intersections of convex sets II. Israel J. Math. 26, 209–213 (1977). https://doi.org/10.1007/BF03007642

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  • DOI: https://doi.org/10.1007/BF03007642

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