The hyperspace of connected boundary subcontinua of a continuum

摘要

Given a metric continumm X, let CB(X) be the hyperspace of subcontinua of X with connected boundary. In this paper we present results concerning CB(X), first about continua for which every subcontinuum has connected boundary. Then we study continua that only have one-point sets as connected boundary proper subcontinua. Later we include characterizations of arcs and simple closed curves. Finally we give a formula for the number of components of CB(X) for finite graphs. (C) 2020 Elsevier B.V. All rights reserved.