Abstract
We prove that the set of homotopy classes of the paths in a topological ring is a topological ringobject (called topological ring-groupoid). Let p : X → X be a covering map and let X be a topological ring.We define a category UTRCov(X) of coverings of X in which both X and X have universal coverings, and acategory UTRGdCov( π1X ) of coverings of topological ring-groupoid π1X , in which X and R0 = X haveuniversal coverings, and then prove the equivalence of these categories. We also prove that the topologicalring structure of a topological ring-groupoid lifts to a universal topological covering groupoid.
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.
