Wenchao Wu - Department of Mathematics, Ocean University of China, ۲۶۶۱۰۰ Qing- dao, P. R. China
Jinming Fang - Department of Mathematics, Ocean University of China, ۲۶۶۱۰۰ Qing- dao, P. R. China

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

L-fuzzifying topology, L-ordered fuzzifying convergence structure, L-filter, Cartesian-closed category, Reflective subcategory