Lipschitz retractions on symmetric products of trees

Abstract

Given a continuum X and a positive integer n, Fn(X) denotes the hyperspace of non-empty subsets of X with at most n elements, endowed with the Hausdorff metric. In this article, given X a simple m-od, we prove that Fn-1(X) is a (6n +1) - Lipschitz retract of Fn(X) for every n >1, and that Fn-1(X) is a 4-Lipschitz retract of Fn(X) for X a tree and n = 2, 3.