Generalized topology and the family of monotonic maps Gamma (X)

Abstract

In this paper, interesting properties of the generalized topological spaces, generated by the monotonic maps sigma = (cl_{delta }circ int_{delta }),alpha = (int_{delta }circ cl_{delta }circ int_{delta }),pi = (int_{delta }circ cl_{delta }) and beta = (cl_{delta }circ int_{delta }circ cl_{delta }), for any generalized topological space (X,g_{delta }) are deduced and analyzed. Special subfamilies of the family of monotonic maps Gamma (X) are studied and interesting results regarding generalized topologies are obtained.