Concerning n-mutual aposyndesis in hyperspaces

Abstract

Abstract. Given a metric continuum X, let 2 X denote the hyperspace of nonempty closed subsets of X. We prove that 2 X is n-mutually aposyndetic for each n ≥ 1. That is, given n distinct elements of 2 X , there are n disjoint subcontinua of 2 X , each containing one of the elements in its interior.