BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Minani Iragi (University of South Africa) DTSTART:20210929T150000Z DTEND:20210929T160000Z DTSTAMP:20260423T021435Z UID:EmCats/2 DESCRIPTION:Title: A categorical study of quasi-uniform structures\nby Minani Iragi (Unive rsity of South Africa) as part of Em-Cats\n\n\nAbstract\nA topology on a s et is usually defined in terms of neighbourhoods\, or equivalently in ter ms of open sets or closed sets. Each of these frameworks allows\, among ot her things\, a definition of continuity. Uniform structures are topologica l spaces with structure to support definitions such as uniform continuity and uniform convergence. Quasi-uniform structures then generalise this ide a in a similar way to how quasi-metrics generalise metrics\, that is\, by dropping the condition of symmetry.\n\nIn this talk we will show how to vi ew these as constructions on the category of topological spaces\, enabling us to generalise the constructions to an arbitrary ambient category. We w ill show how to relate quasi-uniform structures on a category with closure operators. Closure operators generalise the concept of topological closur e operator\, which can be viewed as structure on the category of topologic al spaces obtained by closing subspaces of topological spaces. This method of moving from Top to an arbitrary category is often called "doing topolo gy in categories"\, and is a powerful tool which permits us to apply topol ogically motivated ideas to categories of other branches of mathematics\, such as groups\, rings\, or topological groups.\n LOCATION:https://researchseminars.org/talk/EmCats/2/ END:VEVENT END:VCALENDAR