Concerning k-mutual aposyndesis in symmetric products

摘要

Given a metric continuum X, let F_n(X) denote the hyperspace of nonempty subsets of X with at most n points. We prove that F_n(X) is k-mutually aposyndetic for every k ≥2 and n≥3. That is, given k distinct elements in F_n(X), there are k disjoint subcontinua of F_n{X), each containing one of the elements in its interior.