Abstract
Fuzzy net-theory and fuzzy ideal-theory are both very important tools in fuzzy topology. In this paper, a new extension of fuzzy convergence is presented. The N-limit point and N-cluster point of an L-fuzzy net (resp. an L-fuzzy ideal), N-closed set and N-open set in an L-fuzzy topological space are defined by means of the near N-compactness, and their various properties and mutual relationships are discussed. The N-convergence theory which is a proper generalization of the Moore–Smith convergence theory in fuzzy setting is established.
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