\(T_i\)-spaces. I
For an \(L\)-topological space \((X, \tau)\) and \(x\in X\), the mapping \({\mathcal N}(x): L^X\rightarrow L\) defined by \({\mathcal N}(x)(f)=int_{\tau}f(x)\) is called the fuzzy neighborhood filter at \(x\). By means of this concept, the authors introduce \(T_0\)-axioms, \(T_1\)-axioms and \(T_2\)-axioms in \(L\)-topological spaces where \(L\) is a complete chain. These separation axioms are good extensions in Lowen's sense. Moreover, the \(T_i\)-axiom implies the \(T_{i-1}\)-axiom for \(i=1,2\).
scientific article; zbMATH DE number 2076138