Shai-yan Zhang - School of Science, Southern Yangtze University, Wuxi, Jiangsu ۲۱۴۱۲۲, People۰ s Republic of China
Cong-hua Yan - school of Math. Sciences, Nanjing Normal Uni- versity, Nanjing Jiangsu ۲۱۰۰۴۶, People۰ s Republic of China

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.

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