L-fuzzy N-convergence structures

Based on a completely distributive lattice L, the concept of L-fuzzy N-convergence structures is introduced. It is shown that the category of L-fuzzy topological spaces can be embedded in the category of L-fuzzy N-convergence spaces. It is also proved the category of (topological) pretopological L-fuzzy N-convergence spaces is isomorphic to the category of (topological) L-fuzzy neighborhood spaces and the former is a bireflective subcategory of the category of L-fuzzy N-convergence spaces.