Extensions of the Stone Duality to the category BooleSp

2020/09/30 by Georgi Dimov, Dimov, Georgi, Elza Ivanova-Dimova +1
Computer Science · Decision Sciences · Mathematics · #06E15 #06E75 #18A40 #18B30 #54B30 #54D45 #54D80 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.2010.00097

openalex publication_date 2020/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A De Vries-type Duality Theorem for Locally Compact Spaces -- II

Related

• Two extensions of the Stone Duality to the category of zero-dimensional Hausdorff spaces
• A De Vries-type Duality Theorem for Locally Compact Spaces -- III
• Some Generalizations of Fedorchuk Duality Theorem -- I
• Categorical Extension of Dualities: From Stone to de Vries and Beyond, I
• Categorical Extension of Dualities: From Stone to de Vries and Beyond, II