Uniform lattices. I: A generalization of topological Riesz spaces and topological Boolean rings

DOI10.1007/BF01764134zbMath0790.06006OpenAlexW2082829593MaRDI QIDQ1191394

Hans Weber

Publication date: 27 September 1992

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01764134

zbMATH Keywords

completenessFatou propertyuniform latticeRiesz spacesseparation propertyconvergence of Cauchy netslocally convex topological Boolean ringslocally solid topological \(l\)-groups

Mathematics Subject Classification ID

Topological lattices, etc. (topological aspects) (54H12) Topological lattices (06B30) Ordered topological structures (06F30)

Related Items (35)

Uniform lattices. II: Order continuity and exhaustivity ⋮ Unnamed Item ⋮ Separating points of measures on effect algebras ⋮ Modular functions on multilattices ⋮ Extension of modular functions and measures ⋮ Lattice uniformities generated by filters ⋮ Lattice uniformities and modular functions on orthomodular lattices ⋮ Liapunov theorem for modular functions ⋮ Valuations on complemented lattices ⋮ Positive operators à la Aumann-Shapley on spaces of functions on D-lattices ⋮ Lyapunov decomposition in \(\mathrm{d}_{0}\)-algebras ⋮ Pseudo-D-lattices and Lyapunov measures ⋮ Pseudo-D-lattices and separating points of measures ⋮ Weakly weighted generalised quasi-metric spaces and semilattices ⋮ Lattice uniformities inducing unbounded convergence ⋮ Lebesgue's dominated convergence theorem in Bishop's style ⋮ A characterization of partial metrizability: Domains are quantifiable. ⋮ Decomposition of measures and modular functions ⋮ On lattices of uniformities ⋮ Unnamed Item ⋮ The Hahn decomposition theorem for fuzzy measures and applications ⋮ Weightable quasi-metric semigroups and semilattices ⋮ Unnamed Item ⋮ On topological MV-algebras and topological \(\ell \)-groups ⋮ Lattice uniformities on effect algebras ⋮ Filter topologies and topological MV-algebras ⋮ An extension theorem for modular measures on effect algebras ⋮ Decomposition of pseudo-effect algebras and the Hammer-Sobczyk theorem ⋮ Modular functions: uniform boundedness and compactness ⋮ Uniform BL-algebras ⋮ The correspondence between partial metrics and semivaluations ⋮ Boolean algebras of lattice uniformities and decompositions of modular functions ⋮ Lyapunov modular functions ⋮ Integration: Uniform structure ⋮ Two extension theorems. Modular functions on complemented lattices

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• Group-valued modular functions
• The lattice of topologies of topological $l$-groups
• R-freie Integrationstheorie. I.
• Integratioonstheorie und quasinormierte Gruppen.

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