Research On The New Separability And Weak Separability In The σ Structure

Topological structure occupies an important position in the study of topolo-gy.In 1997,A.Csaszar first researched the generalized topology,and got many topological characterizations.Then,many topologist began to study generalized topology,and got many valuableresults.In 2013,Y.K.Kim and W.K.Min defined a-structure on the base of generalized topology,and got some interesting results on σ-structure.On the basis of previous scholars,we study The new separation properties of σ-structure and The weak separation properties of a-structure.This paper is parted into three chapters.In Chapter 1,we introduce the background of σ-structure,at the same time,we give the necessary symbols and preliminaries which are used in this paper.In Chapter 2,On the basis of a-space,we give the definitions of the closed sets of gσ,the σ-kernel,the closed sets of Aσ.Then we give the definitions the space ofσ-T1/2,the space of σ-T1/4,the space of σ-T3/8,the space of σ-T3/4,and we discuss their related properties,at the same time,we study some properties and relationships of the new separation in the a-space.In Chapter 3,we give the definitions of a-R0 space,σ-R1 space,the weak space of σ-Ro.Furthermore,we study some properties and relationships of the weak separation in the σ-space.