A selection theorem in metric trees

Asuman G. Aksoy, M. A. Khamsi

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

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 ε M. Here by dH we mean the Hausdroff distance. Many applications of this result are given.

Original languageBritish English
Pages (from-to)2957-2966
Number of pages10
JournalProceedings of the American Mathematical Society
Volume134
Issue number10
DOIs
StatePublished - Oct 2006

Keywords

  • Hyperconvex spaces
  • Metric trees
  • Selection theorems

Fingerprint

Dive into the research topics of 'A selection theorem in metric trees'. Together they form a unique fingerprint.

Cite this