Moore–Smith convergence in (L,M)-fuzzy topology

This paper presents a definition of (L,M)-fuzzy nets and the corresponding (L,M)-fuzzy generalized convergence spaces. It establishes a Moore–Smith convergence in (L,M)-fuzzy topology. It is shown that the category (L,M)-GConv of (L,M)-fuzzy generalized convergence spaces is topological, which embeds the category of (L,M)-fuzzy topological spaces as a reflective subcategory. It also defines a strong (L,M)-fuzzy generalized convergence space and shows that the resulting category S(L,M)-GConv is topological and Cartesian-closed, which also embeds the category of (L,M)-fuzzy topological spaces as a reflective subcategory and can be embedded in (L,M)-GConv as a coreflective subcategory. As a special case, (2,M)-GConv is cartesian-closed.

► It presents a definition of (L,M)-fuzzy nets and the corresponding (L,M)-fuzzy generalized convergence spaces.
► It establishes a Moore–Smith convergence in (L,M)-fuzzy topology.
► It is shown that the category (L,M)-GConv of (L,M)-fuzzy generalized convergence spaces is topological, which embeds (L,M)-FTop as a reflective subcategory.
► It defines a strong (L,M)-fuzzy generalized convergence space and shows that the resulting category is Cartesian-closed. As a special case, (2,M)-GConv is Cartesian-closed.