Abstract and concrete categories
Abstract and concrete categories
A new approach for fuzzy topology (I)
Fuzzy Sets and Systems
L-Fuzzifying topologies as L-topologies
Fuzzy Sets and Systems
One-to-one correspondence between fuzzifying topologies and fuzzy preorders
Fuzzy Sets and Systems
L-fuzzy interiors and L-fuzzy closures
Fuzzy Sets and Systems
Measures of fuzzy compactness in L-fuzzy topological spaces
Computers & Mathematics with Applications
Degrees of fuzzy compactness in L-fuzzy topological spaces
Fuzzy Sets and Systems
A note on α- and α*-Hausdorffness
Fuzzy Sets and Systems
Moore--Smith convergence in (L,M)-fuzzy topology
Fuzzy Sets and Systems
Quasi-coincident neighborhood structure of relative I-fuzzy topology and its applications
Fuzzy Sets and Systems
Net-theoretical convergence in (L,M)-fuzzy cotopological spaces
Fuzzy Sets and Systems
On (L,M)-fuzzy convergence spaces
Fuzzy Sets and Systems
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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.