Uniform continuity and uniform convergence revisited

Analysis Seminar
Wednesday, January 13, 2010 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 269
Gerald Beer – California State University, Los Angeles
Plamen Iliev
Sandro Levi and I have investigated variational strengthenings of uniform continuity and uniform convergence of nets or sequences of functions with respect to a family of subsets of the domain. Out of our theory comes an answer to this basic question: what is the weakest topology stronger than the topology of pointwise convergence in which continuity is preserved under taking limits? We argue that the classical theory constitues a misunderstanding of what is fundamentally a variational phenomenon.