Boundedly UC Spaces and Topologies on Function Spaces

A new interesting topology on graphs of partial maps is introduced. This topology can be considered as a natural extension to a non locally compact setting of former topologies defined by P. Brandi, R. Ceppitelli and K. Back, having applications in mathematical economics, differential equations and in the convergence of dynamic programming models. New characterizations of boundedly Atsuji spaces are given by the coincidence of and the topology τ _ucb of uniform convergence on bounded sets on C(X,Y) and by topological properties of .