The Research On Some Problems Of Fuzzy Irresoute Topological Vector Space And Fuzzifying Sp-topological Space

In this paper,it studies two types of fuzzy topological spaces.The one is the fuzzy irresolute topological vector space defined by fuzzy irresolute mapping on the vector space.The other is the fuzzifying sp-topological space based on the method of logical value semantics..The main content of this paper is as follows:First,this paper defines fuzzy irresolute mapping of fuzzy points and researches its properties.It gives the concept of the fuzzy irresolute topological vector space and proves the fuzzy topological translation invariance of fuzzy irresolute topological vector space.Second,this paper gives the concepts of the fuzzy semi Q-neighborhood system and fuzzy semi Q-neighborhood base.And it describes the fuzzy irresolute topological vector space by?_?-fuzzy semi Q-neighborhood base.On this basis,it defines fuzzy irresolute bounded and fuzzy totally irresolute bounded and researches the linear properties of fuzzy?-irresolute bounded sets.Third,this paper defines the fuzzy irresolute topological vector space on the function space.It proves that there exists the unique topology in the function space between the two fuzzy irresolute topological vector spaces and that the function space and the topology can constitute the fuzzy irresolute topological vector space.Fourth,based on the continuous logic value semantics,it studies the fuzzifying sp-topological space,discusses the properties of fuzzifying sp-open sets,sp-neighborhood,sp-closure and sp-interior and gives the concept of fuzzifying sp-continuous mapping.On this basis,it introduces the category FSPTop.Furthermore,it proves that the category FSPTop is the topological category on the category Set.