L-FUZZIFYING TOPOLOGICAL GROUPS

Document Type: Research Paper

Authors

1 School of Science, Southern Yangtze University, Wuxi, Jiangsu 214122, People0 s Republic of China

2 school of Math. Sciences, Nanjing Normal Uni- versity, Nanjing Jiangsu 210046, People0 s Republic of China

Abstract

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
$L$-{\bf FYTPG} is topological over the category of groups {\bf 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.

Keywords


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