Abstract
Given a ring R, we extend Ehrhard’s linearization process by associating to any pre-finiteness space an R-module endowed with a Lefschetz topology. For a semigroup in the category of pre-finiteness spaces, one can endow this R-module with the convolution product to obtain an R-algebra. As examples of pre-finiteness spaces, we study topological spaces with bounded subsets (i.e., included in a compact) taken to be the finitary subsets. We prove that we obtain a finiteness space from any hemicompact space via this construction. As a corollary, any etale Hausdorff groupoid induces a semigroup in pre-finiteness spaces and its associated convolution algebra is complete in the hemicompact case. This is in particular the case for the infinite paths groupoid associated to any countable row-finite directed graph.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.