Helly Theorem and Related Results

• Datum: 2002
• Hauptverfasser: Zelinskii, Yu. B., Зелинский, Ю. Б.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2002
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4045
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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 a...