Helly Theorem and Related Results
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 < k ≤ n, have nonempty intersections. We modify the Helly theorem to fix this issue and investigate the behavior of generalized convex families.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 1, pp 149-153.
Citation Example: Zelinskii Yu. B. Helly Theorem and Related Results // Ukr. Mat. Zh. - 2002. - 54, № 1. - pp. 125-128.