\(T_i\)-spaces. II (Q1433560)

For an \(L\)-topological space \((X, \tau)\) and a nonempty set \(A\subset X\), define the fuzzy neighborhood filter at \(A\) as \({\mathcal N}(A)=\bigvee_{x\in A} {\mathcal N}(x)\). By means of this concept, the authors introduce regularity and normality in \(L\)-topological spaces where \(L\) is a complete chain. These separation axioms are good extensions in Lowen's sense. Moreover normality\(+T_1\) implies regularity and regularity \(+T_1\) implies \(T_2\).