Abstract
Let X and Y be topological spaces and F (X, Y) the set of all functions from X into Y. We study various quasi-uniform convergence topologies U A (A subset of P (X)) on F (X, Y) and their comparison in the setting of Y a quasi-uniform space. Further, we study U-A-closedness and right K-completeness properties of certain subspaces of generalized continuous functions in F (X, Y) in the case of Y a locally symmetric quasi-uniform space or a locally uniform space.