On ?-continuous Mapping And Separation Studies In ?-structures

In 2013, Y. K. Kim and W. K. Min defined ?-structure and ?-open sets on the base of generalized topology, and got some interesting re-sults on ?-structure. In our paper, we define ?-continuous mapping,??₁, ?₂?-continuous mapping, the separation properties of ?-structure and the separation properties of D?-structure, and study their prop-erties. 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 ?-structure, ?-open sets and study the properties of ?-open. We also define ?-continuous mapping and ??₁, ?₂?-continuous mapping by ?-open sets, and study their properties.In Chapter 3, we give the definitions of ?-T₀ space, ?-T₁ space, ?-T₂ space space, ?-T₃ space, ?-T₄ space, ?-D₀ space, ?-D₁ space, ?-D₂ space, ?-R₀ space and ?-R₁ space. Furthermore, we study their topological properties.