On the uniformization of L-valued frames

Abstract

This note discusses the appropriate way of uniformizing the notion of an L-valued frame introduced by A. Pultr and S. Rodabaugh in [Lattice-valued frames, functor categories, and classes of sober spaces, Chapter 6 of Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Kluwer, 2003]. It covers the case of a completely distributive lattice L (which is, in a certain sense, the most general one) and studies the corresponding category of uniform L-valued frames.