An extension of Priestley duality to fuzzy topologies and positive MV-algebras
This provides a theoretical unification for researchers in algebraic logic and fuzzy topology, but is an incremental extension of existing dualities.
The authors extend Priestley duality to categories of fuzzy topological spaces and ordered algebraic structures generalizing bounded distributive lattices, proving a duality that subsumes both classical Priestley duality and a prior duality for MV-algebras.
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.