An extension of de Vries duality to completely regular spaces and compactifications

DOI10.1016/j.topol.2019.02.007zbMath1412.54034OpenAlexW2917724112WikidataQ128334415 ScholiaQ128334415MaRDI QIDQ670153

Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding

Publication date: 18 March 2019

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2019.02.007

zbMATH Keywords

compactificationcomplete Boolean algebraproximitycompact Hausdorff spacecompletely regular spacede Vries dualitymaximal de Vries extension

Mathematics Subject Classification ID

Compactness (54D30) Categorical methods in general topology (54B30) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15) Proximity structures and generalizations (54E05) Boolean algebras with additional operations (diagonalizable algebras, etc.) (06E25)

Related Items (8)

Categorical extension of dualities: from Stone to de Vries and beyond. I ⋮ A unified approach to Gelfand and de Vries dualities ⋮ Unnamed Item ⋮ Extensions of dualities and a new approach to the Fedorchuk duality ⋮ Unnamed Item ⋮ A generalization of Gelfand-Naimark-Stone duality to completely regular spaces ⋮ An extension of de Vries duality to normal spaces and locally compact Hausdorff spaces ⋮ Gelfand-Naimark-Stone duality for normal spaces and insertion theorems

Cites Work

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• A de Vries-type duality theorem for the category of locally compact spaces and continuous maps. I
• Stone duality and Gleason covers through de Vries duality
• Boolean \(\delta\)-algebras and quasiopen mappings
• Proximity frames and regularization.
• Local proximity spaces
• A Proximity Approach to Some Region-Based Theories of Space
• Pierce sheaves and commutative idempotent generated algebras

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