On N-convergence of fuzzy nets

Abstract

In this paper, we define the N-convergence of fuzzy nets in a fuzzy topological space and we use it to give a characterization of some fuzzy topological concepts. We give necessary conditions for the N-convergence of fuzzy nets in a fuzzy topological space and we characterize this N-convergence in a topologically generated fuzzy topological space. We also study some characterizations of fuzzy ultranets and we introduce the concept of subordination between fuzzy nets. We associate to each fuzzy net in X a prefilter on X and conversely, and we give an exhaustive description of the connections between these two theories. We give a theory of fuzzy convergence classes and we characterize fuzzy topologies via some special types of fuzzy convergence classes.