Affine and convex separation problems

Abstract

In this Thesis we study affine and convex separation problems. First, we discuss convex separation theorems in the context of classical convexity, motivated by the result of Baron, Matkowski and Nikodem. Then, we revisit the affine separation theorem of Behrends and Nikodem with an alternative, elementary and self-contained approach. Finally, we discuss a generalized case of convexity, the notion of h-convexity. Our aim is to present similar separation theorems as previously.