Separation axioms in fuzzy topology characterized by bitopologies
Let \(L\) be a fuzzy lattice, \(T\) be a fuzzy topology on \(L\) and \(M(L)\) be the set of all molecules in \(L\). With the fuzzy topological space \((L,T)\) a bitopological space \((M,u,v)\) is associated. A characterization of certain separation axioms for \((L,T)\) in terms of separation axioms for \(M(u,v)\) is given. Some of the results are as follows: \((L,T)\) is molecular \(f\)-\(T_ i\) iff \((M,u,v)\) is ordered-pairwise \(T_ i\), \(i=0,1,2\). \((L,T)\) is molecular \(f\)-\(R_ 0\) (\(f\)-regular, \(f\)-completely regular, \(f\)-normal) iff \((M,u,v)\) is pairwise \(R_ 0\) (regular, completely regular, normal).
scientific article; zbMATH DE number 549409