Extensions of the Stone Duality to the category BooleSp

TL;DR

This paper extends the classical Stone Duality Theorem to the category of zero-dimensional locally compact Hausdorff spaces, providing new duality theorems and building on previous duality results for zero-dimensional Hausdorff spaces.

Contribution

It derives an extension of the Stone Duality to BooleSp and introduces two new duality theorems for this category, expanding the scope of duality theory.

Findings

Extended Stone Duality to BooleSp category.

Derived new duality theorems for zero-dimensional locally compact spaces.

Built upon previous duality results for zero-dimensional Hausdorff spaces.

Abstract

In [G. Dimov and E. Ivanova-Dimova, Two extensions of the Stone Duality to the category of zero-dimensional Hausdorff spaces, arXiv:1901.04537v4, 1--33], extending the Stone Duality Theorem, we proved two duality theorems for the category ZDHaus of zero-dimensional Hausdorff spaces and continuous maps. Now we derive from them the extension of the Stone Duality Theorem to the category BooleSp of zero-dimensional locally compact Hausdorff spaces and continuous maps obtained in [G. Dimov, Some generalizations of the Stone Duality Theorem, Publicationes Mathematicae Debrecen, 80 (2012), 255--293], as well as two new duality theorems for the category BooleSp.