L-FUZZIFYING TOPOLOGICAL GROUPS

The main purpose of this paper is to introduce a concept ofL-fuzzifying topological groups (here L is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding L-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the correspondingL-fuzzifying neighborhood structure of the unit is given. It isshown that the category of L-fuzzifying topological groupsL-{\bf FYTPG} is topological over the category of groups {\bf GRP}with respect to the forgetful functor. As an application, theconclusion that the product of L-fuzzifying topological groups isalso an L-fuzzifying topological group is proved. Finally, it isproved the forgetful functor preserves the product.

Keywords:

L-fuzzifying topological groups , L-fuzzifying topology , L-fuzzifying neighborhood structure , category