On $(n, m)$-Convex Sets
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.
English version (Springer): Ukrainian Mathematical Journal 53 (2001), no. 3, pp 482-487.
Citation Example: Momot I. V., Zelinskii Yu. B. On $(n, m)$-Convex Sets // Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 422-427.