An enriched category approach to many valued topology

In this paper we discuss a basic question in fuzzy set theory: what is a many valued topology on a set X? An answer is presented by interpreting the axioms (two logical formulas) for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of X. As preparation, a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory.