Generalized Topology Cover The Nature And Function Of Insertion

The notion of generalized topology was introduced by the Hungarian mathematician A. Csaszar in2002. It is an important generalization of general topology. After more than ten years, the basic theoretical system of generalized topology has already been established. On the basis of A.Csaszar’s studying, we investigate the insertion of functions and covering properties of generalized topological spaces in this paper.In the first chapter, we introduce some necessary prerequisites.In chapter two, we give some properties of equivalent characterization of generalized countable compact spaces, and discuss relations between generalized countable metacompact-ness (generalized countable paracompactness,generalized countable mesocompactness) and re-finement properties.In chapter three, we investigate function insertion in generalized topological spaces.