LAUSR

Abstract Given a metric continuum X and p ∈ X , we denote by C ( X ) and C ( p , X ) the hyperspace of all subcontinua of X and the hyperspace of all subcontinua of X containing p, respectively. Thus K ( X ) is defined as the collection of all subsets of C ( C ( X ) ) of the form C ( q , X ) where q ∈ X . For a mapping f : X → Y between continua, we consider f ¯ , f ¯ p , f ˜ and f ˇ the natural induced mapping by f at those hyperspaces. In this paper we prove some relationships between the mappings f, f ¯ , f ¯ p , f ˜ and f ˇ for the following classes of mappings: monotone, confluent, weakly confluent, light, open. Moreover, we show that f ¯ p is a monotone mapping.