Lowen spaces

Abstract

An L-fuzzy topological space (X,Δ) is called a Lowen space if Δ has a basis consisting of leveled characteristic functions, that is to say, the elements in Δ of the form aU,a∈L, U⊆X are a basis for Δ. In the case L=[0,1], (X,Δ) is a Lowen space if and only if (X,Δ) 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. © 2000 Academic Press.