Quasi-uniform convergence topologies on function spaces- Revisited

Wafa Khalaf Alqurash, Liaqat Ali Khan

Abstract

Let X and Y be topological space and F(X,Y) the set of all functions from X into Y. We study various quasi-uniform convergence topologies U_{A} (A⊆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.

Keywords

Quasi-uniform space, topology of quasi-uniform convergence on a family of sets, locally uniform spaces, right K-completeness, quasi-continuous functions, somewhat continuous functions.

Subject classification

54C35, 54E15, 54C08

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Universitat Politècnica de València

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