Almost meshed locally connected continua have unique second symmetric product

For a metric continuum X and a positive integer n, we consider the n  -th symmetric product Fn(X)Fn(X) of all nonempty subsets of X with at most n points, with the Hausdorff metric. In this paper we prove for an almost meshed locally connected continuum X, that if Y   is a continuum and F2(X)F2(X) is homeomorphic to F2(Y)F2(Y), then X is homeomorphic to Y. This answers a question by Alejandro Illanes.