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.