Ukrainian Mathematical Journal

, Volume 54, Issue 1, pp 149–153 | Cite as

Helly Theorem and Related Results

  • Yu. B. Zelinskii


By using the classical Helly theorem, one cannot obtain information about a family of convex compact sets in the n-dimensional Euclidean space if it is known that only subfamilies consisting of k elements, 0 < kn, have nonempty intersections. We modify the Helly theorem to fix this issue and investigate the behavior of generalized convex families.


Euclidean Space Relate Result Generalize Convex Nonempty Intersection Helly Theorem 
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    L. Danzer, B. Grunbaum, and V. Klee, Helly's Theorem and Its Relatives, American Mathematical Society, Rhode Island (1963).Google Scholar
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    E. H. Spanier, Algebraic Topology, McGraw-Hill, New York (1966).Google Scholar
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    Yu. B. Zelinskii, Multivalued Mappings in Analysis [in Russian], Naukova Dumka, Kiev (1993).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Yu. B. Zelinskii
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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