$L-$ ORDERED FUZZIFYING CONVERGENCE SPACES

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L-ordered fuzzifying convergence spaces, in which the category of L-fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called the category of principal L-ordered fuzzifying convergence spaces and that of topological L-ordered fuzzifying convergence spaces, and it is shown that they are isomorphic to the category of L-fuzzifying neighborhood spaces and that of L-fuzzifying topological spaces respectively.