Epicomplete archimedean l-groups via a localic Yosida theorem

DOI10.1016/0022-4049(90)90147-AzbMath0718.06005MaRDI QIDQ2639080

James J. Madden, J. Vermeer

Publication date: 1990

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

localeepicompletionYosida representationarchimedean \(\ell \)-groupsepicompleteness

Mathematics Subject Classification ID

Ordered groups (06F15)

Related Items (23)

Representations of Archimedean Riesz spaces. - A survey ⋮ The \(H\)-closed monoreflections, implicit operations, and countable composition, in Archimedean lattice-ordered groups with weak unit ⋮ \(\kappa\)-frames ⋮ An intrinsic characterization of monomorphisms in regular Lindelöf locales ⋮ \(\varepsilon\)-spaces ⋮ Truncated abelian lattice-ordered groups. I: The pointed (Yosida) representation ⋮ The completeness characterization of \(C(\mathcal{L})\), \(\mathcal{L}\) a locale ⋮ From \(\lambda\)-hollow frames to \(\lambda\)-repletions in \(\mathbf{W}\). I: The scaffolding of a completely regular frame ⋮ On the universal completion of pointfree function spaces ⋮ The countable lifting property for Riesz space surjections ⋮ The \(P\)-frame reflection of a completely regular frame ⋮ Composition-closed \(\ell \)-groups of almost-piecewise-linear functions ⋮ Truncated abelian lattice-ordered groups. II: The pointfree (Madden) representation ⋮ A new characterization of the continuous functions on a locale ⋮ \(C\)-epic compactifications ⋮ Monoreflections of Archimedean \(\ell\)-groups, regular \(\sigma\)-frames and regular Lindelöf frames ⋮ The inversion characterizations of \(C(\mathcal{L})\) for a locale \(\mathcal{L} \) ⋮ Monomorphisms in spaces with Lindelöf filters ⋮ More ring-theoretic characterizations of P-frames ⋮ Comments on monoreflections in unital archimedean lattice-ordered groups and rings ⋮ The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups ⋮ Pointfree pointwise suprema in unital Archimedean \(\ell\)-groups. ⋮ On the localic Yosida representation of an archimedean lattice ordered group with weak order unit

Cites Work

• Epicomplete l-groups
• Amalgamation and epimorphisms in m complete Boolean algebras
• The essential closure of an Archimedean lattice-ordered group
• Epicomplete Archimedean l-Groups and Vector Lattices
• Alexandroff Algebras and Complete Regularity
• Residue class fields of lattice-ordered algebras
• Realcompact spaces and regular σ -frames
• Lindelöf locales and realcompactness
• Frames Associated with an Abelian l-Group
• Dimension Theory for Σ-Frames
• The hulls of representablel-groups andf-rings
• Atomless Parts of Spaces.
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