Minimal Pairs of Convex Sets

Abstract

In this chapter we investigate the elementary properties of minimal pairs of compact convex subsets in topological vector spaces. At the beginning we prove the existence of minimal representatives in every equivalence class of pairs of compact convex sets. Then we show that, in general, no minimal representatives exist for pairs of bounded closed convex sets. At the end of this chapter we prove several necessary and sufficient conditions for the minimality of pairs of compact convex sets.