Displaying similar documents to “Functorial approximation to the lateral completion in archimedean lattice-ordered groups with weak unit”

Completion and closure

David Holgate (2000)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Some comments and examples on generation of (hyper-)archimedean ℓ -groups and f -rings

A. W. Hager, D. G. Johnson (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper systematizes some theory concerning the generation of ℓ -groups and reduced f -rings from substructures. We are particularly concerned with archimedean and hyperarchimedean groups and rings. We discuss the process of adjoining a weak order unit to an ℓ -group, or an identity to an f -ring and find significant contrasts between these cases. In ℓ -groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures that they generate, as illustrated...

Monomorphisms in spaces with Lindelöf filters

Richard N. Ball, Anthony W. Hager (2007)

Czechoslovak Mathematical Journal

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𝐒𝐩𝐅𝐢 is the category of spaces with filters: an object is a pair ( X , ℱ ) , X a compact Hausdorff space and ℱ a filter of dense open subsets of X . A morphism f ( Y , 𝒢 ) → ( X , ℱ ) is a continuous function f Y → X for which f - 1 ( F ) ∈ 𝒢 whenever F ∈ ℱ . This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically...