Study On The Weak * Separation Properties And The Weak ?-continuous Mapping Of ?-structure

Generalized Topology is a generalization of general topology,which has some good properties in generalized topology,at the same time,it has enriched the study of general topology.In 1997,The mathematician A.Csaszar first defined the generalized topology,studied the properties of generalized topological,and obtained many useful results.In 2013,Y.K.Kim and W.K.Min defined ?-structure on the base of generalized topology,and got some results on ?-structure.On the basis of previous scholars,we define the space of ?*-R0,the space of ?*-R1,weak ?-continuous mapping and weak(?1,?2)-continuous mapping,and study some of their properties.This paper is parted into three chapters.In Chapter 1,we introduce the background of ?-structure,at the same time,we give the necessary symbols and preliminaries which are used in this paper.In Chapter 2,we give the definitions of the closed sets of g?*,the space of ?*-R0 and the space of ?*-R1.Then we study their properties.In Chapter 3,we give the definitions of weak ?-continuous mapping,weak ?closure continuous mapping and weak(?1,?2)-continuous mapping.Furthermore,we study their topological properties.