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DTSTART;TZID=America/Los_Angeles:20240919T163000
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DTSTAMP:20260508T180427
CREATED:20240910T035239Z
LAST-MODIFIED:20240910T035239Z
UID:3506-1726763400-1726767000@colleges.claremont.edu
SUMMARY:Analysis seminar: Gerald Beer (CSULA)
DESCRIPTION:Title: A crash course in Bornologies \nAbstract: By a bornology on a nonempty set X\, we mean a family of subsets that contains the singletons\, that is stable under finite unions\, and that is stable under taking subsets. The prototype for a bornology is the so-called metric bornology: the family of metrically bounded subsets of a metric space. Bornologies help us to understand large structure. We enumerate some basic bornologies and give a few applications. We give an old result of S.-T. Hu characterizing the bornologies on a metrizable space that are metric bornologies with respect to some compatible metric\, and give a fairly recent result of J. Cabello-Sanchez characterizing those metric spaces (X\,d) for which UC(X\,R) is a ring. We introduce the notion of bornological convergence of a sequence or net of closed subsets\, of which Attouch-Wets convergence is the prototype\, and give two applications to functional analysis.
URL:https://colleges.claremont.edu/ccms/event/analysis-seminar-gerald-beer-csula/
LOCATION:Estella 2393\, Pomona College\, 610 N. College Ave.\, Claremont\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
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