Stone duality of Lawson compact algebraic L-domain

TL;DR

This paper establishes a Stone duality and a dual equivalence between finitely disjunctive distributive lattices and Lawson compact algebraic L-domains, advancing the understanding of their categorical relationships.

Contribution

It introduces FDD-lattices and applies them to develop a duality and dual equivalence for Lawson compact algebraic L-domains, expanding lattice-domain theory.

Findings

Established a Stone duality for Lawson compact algebraic L-domains.

Developed a dual equivalence between FDD-lattices and Lawson compact algebraic L-domains.

Connected lattice homomorphisms with spectral maps in this duality.

Abstract

In this paper, a subclass of bounded distributive lattices, that is, finitely disjunctive distributive lattices (FDD-lattices) have been introduced. Then we apply it to establish a Stone duality for Lawson compact algebraic L-domains. Furthermore, we develop a dual equivalence between the category of FDD-lattices with lattice homomorphisms and that of Lawson compact algebraic L-domains with spectral maps.