Dendrites with unique hyperspace C2(X)

Abstract

Let Y be a metric continuum. Let C n (Y ) be the hyperspace of nonempty closed subsets of Y with at most n components. In this paper we show that if X is a dendrite with closed set of end points and C 2 (X) is homeomorphic to C 2 (Y ), for some dendrite Y , then X is homeomorphic to Y . This completes the work by David Herrera-Carrasco and FernandoMacías-Romero who previously proved the corresponding result for each n = 2.