Lowen Spaces1

An L-fuzzy topological space X, D.is called a Lowen space if D has a basis consisting of leveled characteristic functions, that is to say, the elements in D of the form aU, agL, U:X are a basis for D. In the case Lsw0, 1x, X, D.is a Lowen space if and only if X, D.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