In this paper, we show that any stratified L -topological group G, is uniformizable. That is, we define, using the family of prefilters which corresponds the fuzzy neighborhood filter at the identity element of G,, unique left and right invariant fuzzy uniform structures on G compatible with the fuzzy topology . On the other hand, on any group G , using a family of prefilters on G fulfills certain conditions, we construct those left and right fuzzy uniform structures which induce a stratified fuzzy topology on G for which G, is a stratified L -topological group and this family of prefilters coincides with the family of prefilters corresponding to the fuzzy neighborhood filter at the identity element of G,. Moreover, we show the relation between the L topological groups and the GTi -spaces, such as: the fuzzy topology of an L -topological group (resp., a separated L -topological group) is completely regular, (resp., ) |
