Distributive Cauchy lattices

DOI10.1007/BF01198525zbMath0539.06008OpenAlexW2087065045MaRDI QIDQ793765

Richard N. Ball

Publication date: 1984

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01198525

zbMATH Keywords

distributive latticescompletionsCauchy structuresorder convergencelattice convergencesMacNeille lattice completion

Mathematics Subject Classification ID

Complete distributivity (06D10) Baire category, Baire spaces (54E52) Complete lattices, completions (06B23) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Topological lattices (06B30)

Related Items (13)

Distinguished extensions of an MV-algebra ⋮ Exact and strongly exact filters ⋮ Unnamed Item ⋮ The Dedekind MacNeille site completion of a meet semilattice ⋮ Maximal essential extensions in the context of frames ⋮ Distinguished extensions of a lattice-ordered group ⋮ Exact filters and joins of closed sublocales ⋮ Separation properties at \(p\) for the topological category of Cauchy spaces ⋮ A note on Cauchy spaces ⋮ Notes on exact meets and joins. ⋮ Some general aspects of exactness and strong exactness of meets ⋮ Distributive laws for concept lattices ⋮ Extending semilattices to frames using sites and coverages

Cites Work

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• Completion functors for Cauchy spaces
• Regular completions of Cauchy spaces
• On the order topology in a lattice
• Some considerations on convergence in abelian lattice-groups
• Categorial characterization of the MacNeille completion
• Projective and injective distributive lattices
• Uniform convergence structures
• A decomposition theorem for partially ordered sets
• Distributivity in lattices
• Theory of models with generalized atomic formulas
• Convergence and Cauchy Structures on Lattice Ordered Groups
• Partially Ordered Sets
• A Subdirect-Union Representation for Completely Distributive Complete Lattices

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