On Convergence Classes in L-fuzzy Topological SpacesU

convergence class are characterized by each other. In fuzzy topology L-fuzzy topology., more than 40 papers published in the last ten years were concerned with convergence theory. Among these papers, the problem of convergence class was solved for the case of Lsw0, 1x w7x. Since the neighbor structure, so called ‘‘quasi-coincident neighborhood system,’’ of an L-fuzzy point in an L-fuzzy topological space is in general not directed under the inclusion order, the conditions of convergence class inw0, 1x-fuzzy topology will not be valid any longer in the case of lattice. Moreover, quite different from the cases of 0, 14-fuzzy topology i.e., ordinary topology. and w0, 1x-fuzzy topology, the so called Bolzano]Weierstrass property does not hold, i.e., a net with a cluster point in an L-fuzzy topological space is not still necessary to have a subnet converging to the point. In this paper, a necessary and sufficient condition for the Bolzano]Weierstrass property is produced, the result is also used in a satisfactory theory of convergence classes in L-fuzzy topological spaces, and the associated characterization theorem between L-fuzzy topologies and convergence classes is established.