Title

A Selection Theorem in Metric Trees

Document Type

Article

Department

Mathematics (CMC)

Publication Date

2006

Abstract

In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set-valued mapping T of a metric tree M with convex values has a selection T : M → M for which d(T(x), T(y)) ≤ dH(T(x), T(y)) for each x, y ∈ M. Here by dH we mean the Hausdroff distance. Many applications of this result are given.

Rights Information

© 2006 American Mathematical Society