An extension of Stone Duality to fuzzy topologies and MV-algebras

Abstract

In this paper we introduce the concept of MV-topology, a special class of fuzzy topological spaces, and prove a proper extension of Stone Duality to the categories of limit cut complete MV-algebras and Stone MV-spaces, namely, zero-dimensional compact Hausdorff MV-topological spaces. Then we describe the category of limit cut complete MV-algebras, and show that it is a completion—namely, a reflective subcategory with faithful reflection—of the category of semisimple MV-algebra. Last, we compose our duality with other known ones, thus obtaining new categorical equivalences and dualities involving categories of MV-algebras.