L-FUZZY VERSION OF STONES REPRESENTATION THEOREM FOR DISTRIBUTIVE LATTICES

In this paper the category of L-fuzzy locales is introduced which is proved to play the same role with respect to stratified L-fuzzy topological spaces as that locales play for topological spaces. Secondly, Stone's representation theorem for distributive lattices is generalized to the L-fuzzy case, and the notion of L-fuzzy spectrum of distributive lattices is introduced and its properties are systematically studied; moreover, the harmony between the localic version of Stone's representation theorem and spectral spaces of distributive lattices is also valid in the L-fuzzy case.