ON CO-OPTIMAL LIFTS IN THE CATEGORY OF FUZZY NEIGHBORHOOD SPACES

The category FNS of fuzzy neighbourhood spaces and their continuous fu nctions is closed under the formation of optimal and co-optimal lifts in the larger topological category FTS of fuzzy topological spaces. Bu t, while the fuzzy neighbourhood system and the level topologies of an optimal lift of a source in FNS have simple descriptions in terms of the fuzzy neighbourhood systems and the level topologies, respectively , of the source spaces, analogous descriptions are yet to be given for both constructs for a co-optimal lift of a sink in FNS. We here estab lish such descriptions, with the help of a functor, introduced earlier by one of us, with codomain FNS and domain another full subcategory o f FTS, the category FNBS of fuzzy neighbourhood-base spaces.