Helly Theorem and Related Results - Zelinskii, Yu. B. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
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.