Theoretical Statistics and Mathematics Unit, ISI 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.