Categories isomorphic to [formula omitted]- FTOP

Abstract

In this paper, our purpose is twofold. First, we deal with the local structure of L -fuzzy topology. Hence, modifying the idea of quasi-coincident neighborhood in L -topology, we concretely create an axiomatic system of neighborhood in L -fuzzy topology. Thus we find the category L - FQN of topological L -fuzzy quasi-coincident neighborhood spaces and appropriate continuous maps, which is isomorphic to the category L - FTOP, where L is fuzzy lattice. Further we prove that the category L - FQN is concretely bireflective in another category L - PrFQN constructed in the paper and L - PrFQN is topological category over SET. Secondly, to establish the relation between L - FTOP and L - TOP, we construct two categories L - AITOP and LaTQN. It is proved that L - AITOP is isomorphic to L - FTOP, in particular, when L is fuzzy lattice with locally multiplicative property, LaTQN is isomorphic to L - FTOP.