De Vries algebras and compact regular frames
type: Item
instance of: scholarly article
title: De Vries algebras and compact regular frames
zbMATH Open document ID: 1263.06003
author: Guram Bezhanishvili
published in: Applied Categorical Structures
publication date: 2013-01-02T00:00:00Z
review text: It is proved that the category of de Vries algebras is equivalent to the category of compact regular frames. Alhough this result can be deduced from the existing literature, the proof would go via employing the category of compact Hausdorff spaces and depends on the axiom of choice. In this paper a new proof is proposed which is direct and avoids usage of the axiom of choice. It is also proved that the category of completely regular de Vries algebras is equivalent to the category of compact completely regular frames. Other results are that the category of zero-dimensional de Vries algebras is equivalent to the category of zero-dimensional compact frames; and that the category of extremally disconnected de Vries algebras is equivalent to the category of extremally disconnected compact regular frames.
reviewed by: Ganna Kudryavtseva
Mathematics Subject Classification ID: 06D22
zbMATH DE Number: 6121296
zbMATH Keywords: point-free topology
zbMATH Keywords: duality theory
zbMATH Keywords: compact Hausdorff space
MaRDI profile type: Publication
full work available at URL: s10485-011-9252-5
OpenAlex ID: W2022860141
cites work: Compactification of Frames
cites work: Q3927875
cites work: Q4883943
cites work: Stone duality and Gleason covers through de Vries duality
cites work: Projective topological spaces
cites work: Atomless Parts of Spaces.
cites work: Q3965241
cites work: Q4215784
cites work: Q5813695
cites work: The Theory of Representation for Boolean Algebras
cites work: Q5768904
DOI: 10.1007/S10485-011-9252-5
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description: scientific article; zbMATH DE number 6121296