Sharp Finiteness Principles For Lipschitz Selections

Abstract

Let $${(\mathcal{M}, \rho) }$$ be a metric space and let Y be a Banach space. Given a positive integer m, let F be a set-valued mapping from $${\mathcal{M}}$$ into the family of all compact convex subsets of Y of dimension at most m. In this paper we prove a finiteness principle for the existence of a Lipschitz selection of F with the sharp value of the finiteness constant.