An extension of Priestley duality to fuzzy topologies and positive MV-algebras

TL;DR

This paper extends Priestley Duality to fuzzy topologies and positive MV-algebras, broadening the classical dualities to more general algebraic and topological structures.

Contribution

It generalizes existing dualities by extending Priestley Duality to fuzzy topological spaces and positive MV-algebras, unifying several duality theories.

Findings

Extended Priestley Duality to fuzzy topologies and ordered algebraic structures.

Unified duality frameworks for bounded distributive lattices and MV-algebras.

Connected classical and fuzzy duality theories in a common framework.

Abstract

We extend Priestley Duality to suitable categories of fuzzy topological spaces and ordered algebraic structures that generalize bounded distributive lattices. The duality we prove extends not only classical Priestley Duality between Priestley Spaces and bounded distributive lattices, but also the duality between limit cut complete MV-algebras and Stone MV-topological spaces (proved by the second author in a previous paper) which, on its turn, is an extension of classical Stone Duality.