Abstract
AbstractFor separable ‐algebras and , we define a topology on the set consisting of homotopy classes of asymptotic morphisms from to . This gives an enrichment of the Connes–Higson asymptotic category over topological spaces. We show that the Hausdorffization of this category is equivalent to the shape category of Dadarlat. As an application, we obtain a topology on the ‐theory group with properties analogous to those of the topology on . The Hausdorffized ‐theory group is also introduced and studied. We obtain a continuity result for the functor , which implies a new continuity result for the functor .
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.
