Some Studies On Lattice-valued Fuzzifying Topological Linear Spaces

As one of the important branches of modern analysis,topological linear space is widely used in mathematics and other disciplines,such as functional analysis,theoretical physics,modern engineering theory and so on.With the development of research,people have extended it to the background of multivalued sets.The main work of this paper is as follows:(1)The properties of a base of the zero element L-fuzzifying neighborhood B ? in L-fuzzifying topological linear space(X,?)are studied.Meanwhile,this paper prove that the set-value mappinB?:2X?L satisfying these properties can generate an L-fuzzifying topological linear space(X,?B?),so that P={px|x?X} is the corresponding L-fuzzifying neighborhood structure and one of its bases of zero element L-fuzzifying neighborhood is B ?;(2)L-fuzzifying convex on linear space is defined,and its related algebraic properties are studied used lattice-valued logic semantics;(3)The equivalent conditions of T1 and T2 separation degree in L-fuzzifying topological linear space(X,?)are given respectively,and the Regularity and T3 separation degree in L-fuzzifying topological linear space are defined.At the same time,it is proved that the Regularity of any L-fuzzifying topological linear space is 1,and discuss that Ti(i=0,1,2,3)are mutually equivalent.