TOPOLOGICAL REPRESENTATION FOR FUZZY TOPOLOGICAL-SPACES

Let L be a completely distributive complete lattice with universal bounds 0 and 1 such that 0 not-equal 1. Let us denote by X*(L) the set of all prime proper filters of L. To every L-fuzzy topological space (X, tau) one can associate a topological space (X*(L), T*). One obtains a covariant functor from the category CG(L) into the category of topological spaces. We discuss further how far one can go in this direction following ideas in [2].