Momot I. V.
Ukr. Mat. Zh. - 2003. - 55, № 2. - pp. 284=287
We investigate a class of compact sets convex with respect to a certain family of planes. For compact sets that satisfy the condition of acyclicity of sections by a certain collection of two-dimensional planes, we prove their generalized convexity.
Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1710-1713
We prove a complex analog of the classical Klee theorem for strongly linearly convex closed sets.
Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 422-427
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.