The Study Of Topological Property And Category Property In Fuzzifying Topological Space And Intuitionistic Fuzzifying Topological Space

In this thesis, the main work is to discuss the θ-separation,θ-convergence corresponding properties relationed with θ-open set inFuzzifying topological space.In addition,intuitionistic topological spaceseparation and related category properties are discussed.The primary studiesare the following:(1)Fuzzifying topology from a new direction with the semantic methodof continuous-valued logic is inquired by Professor Mingsheng Ying in1991,followed by many scholars at home and abroad topology extensive andin-depth study. In1996, Zhangguang Ji introduced the concepts of Fuzzifyingθ-open set, θ-neighborhood system. In1999, Zhangguang Ji introducedθ-Continous Function and θ-Compactness in Fuzzifying Topological Space.In2004M.Caldas, S.Jafari study some properties of θ-open sets in generaltopological spaces. On the basis of this, the concepts and properties ofθ-neighborhood system and θ-derived set,θ-boundary and θ-internal ofFuzzifying Topological Space are studied in the further way in this thesis. Inaddition, the θ-separation、θ-convergence are proposed.(2)The concept of intuitionistic fuzzy sets is proposed by Atanassovk in1983.The intuitionistic fuzzy topological space(which is the promotion ofChang fuzzy topological spaces)is introduced and the correspondingproperties of the intuitionistic fuzzy topological space are discussed by Cokein1997.The Moore-Smith convergence theory and the base and sub-base ofthe intuitionistic topological space and intuitionistic topology are studied byZhufeng Mei in2011.On this basis,the separation of intuitionistic Fuzzifyingtopological space and the conclusion of intuitionistic Fuzzifying topologicalcategory is isomorphic to the intuitionistic neighborhood space are studied.