The affine separation problem revisited

The aim of this note is to characterize in terms of inequalities those pairs of real functions (acting on a convex subset of a vector space) that possess an affine separator. The main result is originally due to Behrends and Nikodem. Their method is based on the Hahn–Banach Theorem and a variant of the Helly Theorem. In our approach, a direct and independent proof is presented via the Radon and the Helly Theorems.