Strong separation and strong countability in fuzzy topological spaces

Given a fuzzy topological space (X, δ), we introduce new notions of fuzzy separation and fuzzy countability, using the family of its level-topologies: {ιt(σ): t ϵ [0, 1)}. We check that these are well-defined fuzzy topological concepts and we compare them with the analogous fuzzy ones introduced in the literature. We verify that these notions are not equivalent, and we give a large number of examples which illustrate this fact.