Boundedly UC spaces and topologies on function spaces

A new interesting topology tau_B 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 coincidence of tau_B and the topology tau_ucb of uniform convergence on bounded sets on C(X, Y) and by topological properties of tau_B.