d-Boolean algebras and their bitopological representation

TL;DR

This paper develops a duality theory linking d-Boolean algebras with a class of compact, zero-dimensional T0 bitopological spaces, extending classical Stone duality to a bitopological context.

Contribution

It introduces d-Boolean algebras and establishes a dual equivalence with certain bitopological spaces, generalizing existing dualities in topology and algebra.

Findings

D-Boolean algebras are defined and characterized.

A duality between d-Boolean algebras and specific bitopological spaces is proved.

The duality generalizes classical Stone duality to a bitopological setting.

Abstract

We present a Stone duality for bitopological spaces in analogy to the duality between Stone spaces and Boolean algebras, in the same vein as the duality between d-sober bitopological spaces and spatial d-frames established by Jung and Moshier. Precisely, we introduce the notion of d-Boolean algebras and prove that the category of such algebras is dually equivalent to the category of compact and zero-dimensional bitopological spaces satisfying the T0 separation axiom.