Regularity and normality of \((L,M)\)-fuzzy topological spaces (Q429389)

The author introduces the concept of the so-called new \(T_0\)-axiom, of \(T_1\), \(T_2\), regularity and normality in an \((L,M)\)-fuzzy topological space, where \(L\) and \(M\) are completely distributive lattices with order-reversing involution. The notions of regularity and normality that are introduced here generalize the concepts of regularity and normality introduced earlier in \(L\)-topological spaces attributed to \textit{B. Hutton} and \textit{I. Reilly} [Fuzzy Sets Syst. 3, 93--104(1980; Zbl 0421.54006)]. All separation axioms introduced are studied in the context of \((L,M)\)-fuzzy metric spaces [\textit{F.-G. Shi}, Indian J. Math. 52, No. 2, 231--250 (2010; Zbl 1204.54007)].