$L-$ordered Fuzzifying Convergence Spaces

Abstract

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