Comparing n-fold and m-fold hyperspaces

Let X be a metric continua. Let Cn(X) be the hyperspace of nonempty closed subsets of X with at most n components. In this paper we suppose that Cn(X) is finite-dimensional, Cn(X) is homeomorphic to Cm(Y) and n⩽m. We prove that m⩽2n and we give sufficient conditions on X under which we can assert that n=m.