Geometric Form of the Hahn–Banach Theorem for Generalized Convexity
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.
English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 2, pp 347-351.
Citation Example: Momot I. V. Geometric Form of the Hahn–Banach Theorem for Generalized Convexity // Ukr. Mat. Zh. - 2003. - 55, № 2. - pp. 284=287.