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.
How to Cite
Zelinskii, Y. B. “Helly Theorem and Related Results”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 54, no. 1, Jan. 2002, pp. 125-8, https://umj.imath.kiev.ua/index.php/umj/article/view/4045.
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