A generalization of the Stone duality theorem

DOI10.1016/j.topol.2017.02.041zbMath1421.54020arXiv1603.00932OpenAlexW2963374951MaRDI QIDQ2400865

Dimiter Vakarelov, Elza Ivanova-Dimova, Georgi D. Dimov

Publication date: 30 August 2017

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

Full work available at URL: https://arxiv.org/abs/1603.00932

zbMATH Keywords

Stone space(complete) Boolean algebra(pre)contact algebra2-(pre)contact spaceStone 2-spaceStone adjacency space(closed) relations(Stone) dualityC-semiregular spacesmereocompact space.u-points

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Compactness (54D30) Lower separation axioms ((T_0)--(T_3), etc.) (54D10) Proximity structures and generalizations (54E05) Stone spaces (Boolean spaces) and related structures (06E15) Logical aspects of Boolean algebras (03G05) Topological representations of algebraic systems (54H10)

Related Items (4)

Base and weight of Boolean \(\mathrm{I}\)-contact algebras ⋮ On dimension andweight of a local contact algebra ⋮ Subordination Tarski algebras ⋮ Dynamic Contact Algebras with a Predicate of Actual Existence: Snapshot Representation and Topological Duality

Cites Work

• Boolean connection algebras: A new approach to the Region-Connection Calculus
• Boolean \(\delta\)-algebras and quasiopen mappings
• Remarks on contact relations on Boolean algebras
• Topological representation of precontact algebras and a connected version of the Stone duality theorem. I.
• Region-based theory of discrete spaces: A proximity approach
• Proximity structures and grills
• A representation theorem for Boolean contact algebras
• Mereocompactness and Duality for Mereotopological Spaces
• The Theory of Representation for Boolean Algebras
• Relational Methods in Computer Science
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