Back to Calendar

Wednesday, March 4, 2015

4:15 PM - 5:30 PM (ET)

ESC 638

Event Type

Lecture

Contact

Philip Scowcroft, pscowcroft@wesleyan.edu, x2172

Department

Academic

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=48507

Abstract: A vector lattice is a real linear space with a compatible lattice-order.Examples are C(X) (continuous functions from the topological space X to the reals ),and any abstract 'measurable functions mod null functions'.The sigma property of a vector lattice A is (s) For each sequence (a(n)) in A+,there are a sequence (p(n)) of positive reals and a in A,for which p(n)a(n) < a for each n.Examples:C(X) for compact X (trivial);Lebesgue Measurable mod Null (not trivial;connected with Egoroff's theorem).An application:If a quotient A/I has (s),the the quotient map lifts countable disjoint sets to disjoint sets.We consider which C(X) have (s),for example: For discrete X,C(X) has (s) iff the cardinal of X < the bounding number b. For metrizable X ,C(X) has (s) iff X is locally compact and each open cover has a sub cover of size