Geometric Form of the Hahn–Banach Theorem for Generalized Convexity - Momot, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
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.