The Sufficiency And Necessity Condition Of The Total T₂ Space Is The S-closed Space And The Study On The Open Sub Space In The Fuzzifying Topology System

In this thesis, we mainly explore the sufficiency and necessity condition of the total T₂ space is the S-closed space, and discuss the relationships of the open set, interior, closure, regular open set between the sub space in the Ying Mingsheng's Fuzzifying topology system. In the process of my study, I have obtained some productive results.This paper consists of five parts.Chapter one: IntroductionChapter two: In this chapter, the basic definitions and necessary lemmas are introduced in the paper.Chapter three: In this chapter, we give the proof of the sufficiency and necessity condition of the total T₂ space is the S-closed space.Chapter four: In this chapter, we Supply the text [6] did not give the proof of T3 and T_3(1/2) both cases.Chapter five: In this chapter, we discuss the relationships of the open set, internal, closure, regular open set between the sub space in the Ying Mingsheng's Fuzzifying topology system.