On (L, M)-fuzzy convergence spaces

This paper presents a definition of (L, M)-fuzzy convergence spaces. It is shown that the category (L, M)-FC of (L, M)-fuzzy convergence spaces, which embeds the category (L, M)-FTop of (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)-fuzzy convergence spaces is isomorphic to the category of (topological) (L M)-fuzzy quasi-coincident neighborhood spaces. Moreover, the relations among (L, M)-fuzzy convergence spaces, pretopological (L, M)-fuzzy convergence spaces and topological (L, M)-fuzzy convergence spaces are investigated in the categorical sense. (C) 2013 Elsevier B.V. All rights reserved.