Abstract
We prove that for every separable, 0-dimensional metrizable space X without isolated points, such that every compact subset of it is scattered, the cocompact topology on the hyperspace of X does not coincide with the upper Kuratowski topology—that is, X is dissonant. In particular, it follows that the rational line is dissonant, and that there exist dissonant, hereditarily Baire, separable metrizable spaces.
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.
