On $(n, m)$-Convex Sets

  • Yu. B. Zelinskii
  • I. V. Momot


We investigate the class of generalized convex sets on Grassmann manifolds, which includes known generalizations of convex sets for Euclidean spaces. We extend duality theorems (of polarity type) to a broad class of subsets of the Euclidean space. We establish that the invariance of a mapping on generalized convex sets is equivalent to its affinity.
How to Cite
Zelinskii, Y. B., and I. V. Momot. “On $(n, m)$-Convex Sets”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 3, Mar. 2001, pp. 422-7, https://umj.imath.kiev.ua/index.php/umj/article/view/4263.
Research articles