Seminar at SMU Delhi
April 22, 2015 (Wednesday) ,
3:30 PM at Webinar
Speaker:
Gerald Beer,
California State University Los Angeles
Title:
Graphical convergence of continuous functions
Abstract of Talk
Let X and Y be metrizable spaces. We show that
convergence of a net of continuous functions to a continuous
limit in the graph topology for C(X,Y) is equivalent to the
uniform convergence of the net of associated distance
functionals for the graphs with respect to each compatible
metric for the product of X and Y equipped with the
product topology. Remarkably, no weaker convergence results
if uniform convergence is replaced by pointwise convergence
in the last statement. This is a joint work with Som
Naimpally.