Abstract
For a regular space X, the hyperspace (CL(X),τF) (resp., (CL(X),τV)) is the space of all nonempty closed subsets of X with the Fell topology (resp., Vietoris topology). In this paper, we give the characterization of the space X such that the hyperspace (CL(X),τF) (resp., (CL(X),τV)) with a countable character of closed subsets. We mainly prove that (CL(X),τF) has a countable character on each closed subset if and only if X is compact metrizable, and (CL(X),τF) has a countable character on each compact subset if and only if X is locally compact and separable metrizable. Moreover, we prove that (K(X),τV) have the compact-Gδ-property if and only if X have the compact-Gδ-property and every compact subset of X is metrizable.
Sign-in/Register to access full text options 
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 callDisclaimer: 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.
