Topological representation of precontact algebras and a connected version of the Stone duality theorem. I.

DOI10.1016/j.topol.2017.01.019zbMath1377.54040arXiv1508.02220OpenAlexW2963436654MaRDI QIDQ2363289

Dimiter Vakarelov, Georgi D. Dimov

Publication date: 13 July 2017

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

Full work available at URL: https://arxiv.org/abs/1508.02220

zbMATH Keywords

Stone dualityStone space(complete) Boolean algebra(extremally) connected space(pre)contact algebra2-(pre)contact spaceC-semiregular spaces (extensions)Stone 2-spaceStone adjacency space

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Compactness (54D30) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Lower separation axioms ((T_0)--(T_3), etc.) (54D10) Stone spaces (Boolean spaces) and related structures (06E15) Extremally disconnected spaces, (F)-spaces, etc. (54G05) Topological representations of algebraic systems (54H10)

Related Items (7)

A generalization of the Stone duality theorem ⋮ On dimension andweight of a local contact algebra ⋮ Subordinations on bounded distributive lattices ⋮ Relational representation for subordination Tarski algebras ⋮ Extensions of dualities and a new approach to the Fedorchuk duality ⋮ Irreducible equivalence relations, Gleason spaces, and de Vries duality ⋮ Admissibility of \(\Pi_2\)-inference rules: interpolation, model completion, and contact algebras

Cites Work

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• Generalized region connection calculus
• Region-based topology
• Boolean connection algebras: A new approach to the Region-Connection Calculus
• Boolean \(\delta\)-algebras and quasiopen mappings
• Region-based theory of discrete spaces: A proximity approach
• Proximity structures and grills
• A representation theorem for Boolean contact algebras
• A Proximity Approach to Some Region-Based Theories of Space
• SHEAVES OF BANACH SPEACES
• The Theory of Representation for Boolean Algebras
• Relational Methods in Computer Science

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