Separation Axioms In L-topological Spaces

In this thesis, the main purpose is to discuss the separation in L-topological spaces(L-Fuzzy topological spaces)in the further way and discuss the derived set and consecution in I-Fuzzy topological spaces. The primary studies in this paper are the following:(1)Separation axioms are very important in L-topological spaces. Steen L A,etal.definedT_2(1/2)separation axioms in classical topological spaces,and Chen shui-li , Meng guang-wu and You fei expand it onto L-topological spaces. In this thesis, first, I define T_2(1/3) separation axioms in classical topological spaces, and point out that T_2(1/3)separation axioms is equal to T_2(1/3)separation axioms in classical topological spaces. Second, I define T_2(1/3)separation axioms in L-topological spaces, and point out that T_2(1/3)separation axioms is not equal to T2 12 separation axioms in L-topological spaces. In the same time, I define ST_2(1/3),LT_2(1/3)separation axioms in L-topological spaces, and discuss the relationship with other separation axioms, and prove that they are Lowen good extension,and study some properties of them.(2)Professor JI Zhi-fang defined T₃^# separation axioms. In this thesis, I continue to discuss its some properties, and define a new separation axioms: T₃^?separation axiom which is between T₃^# separation axioms and T₃ separation axioms, and prove that the category of T₃^# L-fuzzy topological spaces are the category of having product and coproduct.