Fuzzy Inductive Topology And Fuzzy Consistent Structure

The theory of fuzzy topological linear space is an important part of fuzzy func-tional analysis spaces.Based on Lukasiewics logical semantics method,In this thesis,the fuzzifying inductive topology and the fuzzifying uniform structure in the fuzzifying topological linear space are studied deeply.The main results are as follows:Firstly,the concept of upper bound topology determined by a family of fuzzifying linear topologies in linear space is introduced,and the characteri-zation of the zero neighborhood system of upper bound fuzzifying topology is obtained.It is proved that the degree of boundedness and total boundedness of a set in linear space are equal to the lower of boundedness and total bounded-ness of the set in factor space.The properties of level topology of the upper bound fuzzified topology are studied.It is proved that the level topology of the upper bound fuzzified topology equals the upper bound of the level topology of the factor space.Secondly,the concepts of fuzzifying generalized inductive topology and fuzzifying inductive topology are introduced.The uniqueness of fuzzifying generalized inductive topology in some sense is explained.Considering the fuzzifying inductive topology determined by a single operator,i.e.the fuzzi-fying quotient topology,the characterization of its fuzzifying neighborhood system is obtained.The research has laid a theoretical foundation for further research on the fuzzifying inductive limit.Finally,the relationship between two fuzzifying uniform structures in fuzzi-fying topological space is studied and their equivalence is proved.The fuzzi-fying uniform structure in fuzzifying topological linear space is introduced.It is proved that the continuity and uniform continuity of linear operators in fuzzifying topological linear space are equal.