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.
Castañeda, E., & Illanes, A. (2006). Finite graphs have unique symmetric products. Topology and Its Applications, 153(9), 1434–1450. https://doi.org/10.1016/j.topol.2005.04.006