Enriched (L,M)-fuzzy convergence spaces

Abstract

This paper presents a definition of enriched (L, M)-fuzzy convergence spaces. It is shown that the resulting category E(L, M)-FC is a Cartesian closed topological category, which can embed the category E(L, M)-FTop of enriched (L, M)- fuzzy topological spaces as a reflective subcategory. Also, it is proved that the category of topological enriched (L, M)-fuzzy convergence spaces is isomorphic to E(L, M)-FTop and the category of pretopological enriched (L, M)-fuzzy convergence spaces is isomorphic to the category of enriched (L, M)-fuzzy quasi-coincident neighborhood spaces.