Finite graphs have unique symmetric products

Abstract

Let X be a metric continuum and let Fn(X) be the nth symmetric product of X(Fn(X) is the hyperspace of nonempty subsets of X with at most n points). In this paper we prove that if Fn(X) is homeomorphic to Fn(Y), where X is a finite graph and Y is a continuum, then X is homeomorphic to Y. © 2005 Elsevier B.V. All rights reserved.