Stone duality of Lawson compact algebraic L-domain

TL;DR

The paper develops a Stone-type duality between finitely disjunctive distributive lattices ($FDD$-lattices) and Lawson compact algebraic $L$-domains by introducing $CO(-)$ and $pt(-)$ constructions. It proves that for a Lawson compact algebraic $L$-domain $L$, the lattice $CO(L)$ is an $FDD$-lattice and $pt(L)$ is a Lawson compact algebraic $L$-domain, and it constructs natural isomorphisms linking these two viewpoints. This yields a dual equivalence between the category of $FDD$-lattices with lattice homomorphisms and the category of Lawson compact algebraic $L$-domains with spectral maps. The results extend Stone duality to a domain-theoretic setting, providing a categorical bridge between lattice-based and topological/domain representations of these structures.

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.

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Theorems & Definitions (26)

• Definition 2.1
• Definition 2.2
• Definition 2.3
• Theorem 2.4
• Lemma 2.5
• Theorem 2.6
• Definition 3.1
• Definition 3.2
• Definition 3.3
• Definition 3.4