Abstract
Using the notion of topologically stable points, it is proved that every equicontinuous pointwise topologically stable homeomorphism of a compact metric space is persistent. Also, using the notion of strong topologically stable points of a Borel probability measure, it is shown that every pointwise strong topologically stable Borel probability measure with respect to an equicontinuous homeomorphism of a compact metric space is strong persistent. Further, it is established that any homeomorphism of as well as that of (0,1) does not admit any uniformly expansive point. Finally, these results are used to show that the unit circle does not admit any expansive homeomorphism.
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.
