Lowen spaces

An L-fuzzy topological space (X, Delta) is called a Lowen space if Delta has a basis consisting of leveled characteristic functions, that is to say, the elements in Delta of the form aU, a is an element of L, U subset of or equal to X are a basis for Delta. In the case L = [0, 1], (X, Delta) is a Lowen space if and only if (X, Delta) is a fuzzy neighborhood space in the sense of Lowen. It is proved in this paper that the category of Lowen spaces is a simultaneously bireflective and bicoreflective subcategory of the category of L-fuzzy topological spaces, and it is isomorphic to the category of L-fuzzifying topological spaces. Several characterizations of these spaces are given. (C) 2000 Academic Press.