Properties of Convex Sets: A Glimpse

Abstract

Convex sets play a very important role in geometry. In this section we state and prove some of the “classics� of convex affine geometry: Carathéodory’s theorem, Radon’s theorem, and Helly’s theorem. These theorems share the property that they are easy to state, but they are deep, and their proof, although rather short, requires a lot of creativity. We will return to convex sets when we study Euclidean geometry.