# Uniformly continuous maps between ends of {\mathbb{R}}-trees

Research paper by Álvaro Martínez-Pérez, Manuel A. Morón

Indexed on: 09 Oct '08Published on: 09 Oct '08Published in: Mathematische Zeitschrift

#### Abstract

There is a well-known correspondence between infinite trees and ultrametric spaces which can be interpreted as an equivalence of categories and comes from considering the end space of the tree. In this equivalence, uniformly continuous maps between the end spaces are translated to some classes of coarse maps (or even classes of metrically proper Lipschitz maps) between the trees.