A Generalization of the Stone Duality Theorem

TL;DR

This paper introduces a new duality theorem for precontact algebras that generalizes and unifies several existing duality theorems, including Stone duality and recent related results.

Contribution

It presents a broad new duality theorem for precontact algebras, extending and encompassing previous dualities in contact algebra theory.

Findings

Unified duality theorem for precontact algebras

Implication of Stone duality as a special case

Extension to contact and complete contact algebras

Abstract

We prove a new duality theorem for the category of precontact algebras which implies the Stone Duality Theorem, its connected version obtained in arXiv:1508.02220v3, 1-44 (to appear in Topology Appl.), the recent duality theorems of Bezhanishvili, G., Bezhanishvili, N., Sourabh, S., Venema, Y. and Goldblatt, R. and Grice, M, and some new duality theorems for the category of contact algebras and for the category of complete contact algebras.