Separation axioms in [formula omitted]-fuzzy topological spaces (I): [formula omitted] and [formula omitted

Abstract

Using the notion of remote neighborhood, we define the separation axioms T 0 and T 1 in L-fuzzy topological spaces ( L-fts). The relations between our definitions, Hutton and Reilly's, and Wang's are discussed, and the separations of Hutton's fuzzy unit interval and Gantner's fuzzy real line are examined. Characterizations of these L-fts are proved and a series of properties of them are investigated. Moreover, some results on minimal T 0 L -fts and T 1 L -fts are established, which will be used immediately in our subsequent discussion.