Advertisement

Ukrainian Mathematical Journal

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

Helly Theorem and Related Results

  • Yu. B. Zelinskii
Article

Abstract

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.

Keywords

Euclidean Space Relate Result Generalize Convex Nonempty Intersection Helly Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    L. Danzer, B. Grunbaum, and V. Klee, Helly's Theorem and Its Relatives, American Mathematical Society, Rhode Island (1963).Google Scholar
  2. 2.
    E. H. Spanier, Algebraic Topology, McGraw-Hill, New York (1966).Google Scholar
  3. 3.
    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

Personalised recommendations