Almost meshed locally connected continua have unique third symmetric product

摘要

For a metric continuum X, we consider the 3-th symmetric product F-3 (X) of all nonempty subsets of X with at most 3 points, with the Hausdorff metric. In this paper we prove for an almost meshed locally connected continuum X, if Y is a continuum and F-3 (X) is homeomorphic to F-3 (Y), then X is homeomorphic to Y. This result completes the work of R. Hernandez-Gutierrez and V. Martinez-de-laVega; D. Herrera-Carrasco, M. de J. Lopez and F. Macias-Romero who previously proved the corresponding result, for each n is an element of N - {3}. (C) 2019 Elsevier B.V. All rights reserved.