Dendrites with unique hyperspace C2 (X)

Abstract

Let Y be a metric continuum. Let Cn (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 C2 (X) is homeomorphic to C2 (Y), for some dendrite Y, then X is homeomorphic to Y. This completes the work by David Herrera-Carrasco and Fernando Macías-Romero who previously proved the corresponding result for each n ≠ 2. © 2008 Elsevier B.V. All rights reserved.