Uniform continuity and uniform convergence revisited

Analysis Seminar
Wednesday, January 13, 2010 - 14:00
1 hour (actually 50 minutes)
Skiles 269
California State University, Los Angeles
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.