INTERSECTIONS BY HYPERPLANES

Let A be a finite nonempty family of nonempty disjoint closed and bounded sets in a Banach space E which is either separable and the conjugate of some Banach space X (i.e. E=X*) or, reflexive and locally uniformly convex. If C denotes the weak*-closed convex hull of ∪ {A:A ∈A} then the set of points in E ∼C through which there is no hyperplane intersecting exactly one member of A is discrete (or empty). © 1969 Hebrew University.