2018
Том 70
№ 6

All Issues

On $(n, m)$-Convex Sets

Momot I. V., Zelinskii Yu. B.

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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.

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.

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