A Selection Theorem in Metric Trees

Authors

Asuman Güven Aksoy, Claremont McKenna CollegeFollow
Mohamed A. Khamsi, University of Texas at El Paso

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)) ≤ d_H(T ^∗(x), T ^∗(y)) for each x, y ∈ M. Here by d_H we mean the Hausdroff distance. Many applications of this result are given.

Rights Information

© 2006 American Mathematical Society

DOI

10.1090/S0002-9939-06-08555-8

Recommended Citation

A.Aksoy, M. A. Khamsi, “A selection theorem in metric trees” Proc. of Amer .Math. Soc. 134 (2006) No. 10, 2957-2966.