UNIQUENESS OF HYPERSPACES OF INDECOMPOSABLE ARC CONTINUA

Given a metric continuum X, we consider the hyperspace Cn(X) of all nonempty closed subsets of X with at most n components. In this paper we prove that if n 6 = 2, X is an indecomposable continuum such that all its proper nondegenerate subcontinua are arcs and Y is a continuum such that Cn(X) is homeomorphic to Cn(Y), then X is homeomorphic to Y (that is, X has unique hyperspace Cn(X))