THE URYSOHN LEMMA FOR FUZZY NEIGHBORHOOD SPACES

The framework FNS of Lowen's fuzzy neighbourhood spaces is a special environment for the study of fuzzy topology. It encompasses its own metrics, uniformities and proximities, among other interesting constructions. This is a fresh and fast growing field of research. It promises to develop quickly to a calculus which combines depth with applicability. Within this framework, we establish the Urysohn Lemma for the Mashhour-Morsi axiom of N-normality. The formulation employs the Mashhour-Morsi N-Euclidean space, as the suitable fuzzy analogue of the real line. The proof makes use of the Artico-Moresco fuzzy proximities, the Lowen fuzzy uniformities and the Mashhour-Morsi axiom of N-complete regularity.