On (L,M)(L,M)-fuzzy convergence spaces

This paper presents a definition of (L,M)(L,M)-fuzzy convergence spaces. It is shown that the category (L,M)(L,M)-FC of (L,M)(L,M)-fuzzy convergence spaces, which embeds the category (L,M)(L,M)-FTop of (L,M)(L,M)-fuzzy topological spaces as a reflective subcategory, is a Cartesian closed topological category. Further, it is proved that the category of (topological) pretopological (L,M)(L,M)-fuzzy convergence spaces is isomorphic to the category of (topological) (L,M)(L,M)-fuzzy quasi-coincident neighborhood spaces. Moreover, the relations among (L,M)(L,M)-fuzzy convergence spaces, pretopological (L,M)(L,M)-fuzzy convergence spaces and topological (L,M)(L,M)-fuzzy convergence spaces are investigated in the categorical sense.