Regularity and normality of (L,M)-Fuzzy topological spaces

In this paper, regularity and normality axioms are introduced in (L,M)-fuzzy topological spaces where L and M are completely distributive lattices with order-reversing involution. Each (L,M)-fuzzy topological space can be regarded to be regular and normal to some degree. The relations among the four separation axioms are investigated. They are equivalent to each other in an (L,M)-fuzzy metric space.