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.