L-FUZZIFYING TOPOLOGICAL GROUPS

The main purpose of this paper is to introduce a concept of L- fuzzifying topological groups (here L is a completely distributive lattice) and discuss some of their basic properties and the structures. We prove that its corresponding L-fuzzifying neighborhood structure is translation invariant. A characterization of such topological groups in terms of the corresponding L- fuzzifying neighborhood structure of the unit is given. It is shown that the category of L-fuzzifying topological groups L-FYTPG is topological over the category of groups GRP with respect to the forgetful functor. As an application, the conclusion that the product of L-fuzzifying topological groups is also an L-fuzzifying topological group is proved. Finally, it is proved the forgetful functor preserves the product.