Regularity and normality of (L,M)-fuzzy topological spaces using residual implication

Abstract

In this paper, the notions of regularity and normality of (L,M)-fuzzy topological spaces are introduced by using residual implication, where L and M are completely distributive De Morgan algebras. It is shown that (L,M)-fuzzy interior operator and (L,M)-fuzzy closure operator can be used to characterize regularity and normality. The relationships among separation axioms of an (L,M)-fuzzy topological space are discussed. Moreover, it is proved that the four separation axioms are equivalent to one another in an (L,M)-fuzzy metric space.