On (n,m)-Convex Sets

Authors

  • Yu. B. Zelinskii
  • I. V. Momot

Abstract

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.

Published

25.03.2001

Issue

Section

Research articles

How to Cite

Zelinskii, Yu. 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.