Abstract

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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.