The order convergence structure

DOI10.1016/j.indag.2011.02.004zbMath1231.06022OpenAlexW2050806675MaRDI QIDQ719616

Jan Harm van der Walt

Publication date: 10 October 2011

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2011.02.004

zbMATH Keywords

Riesz spaceorder-convergenceconvergence structure\(\sigma \)-distributive lattices

Mathematics Subject Classification ID

Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19) Ordered topological structures (06F30) Ordered rings, algebras, modules (06F25) Ordered topological linear spaces, vector lattices (46A40)

Related Items (11)

Algebraic and topological structure of some spaces of set-valued maps ⋮ Unnamed Item ⋮ Net convergence structures with applications to vector lattices ⋮ Differential chain of algebras of generalized functions ⋮ Strong sequential completeness of the natural domain of a conditional expectation operator in Riesz spaces ⋮ The Brezis-Lieb lemma in convergence vector lattices ⋮ Convergence in Riesz spaces with conditional expectation operators ⋮ Full lattice convergence on Riesz spaces ⋮ The order convergence structure ⋮ The existence of fuzzy Dedekind completion of Archimedean fuzzy Riesz space ⋮ A closed graph theorem for order bounded operators

Cites Work

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• The order convergence structure
• Intermediate Riesz spaces
• Order convergence and topological completion of commutative lattice-groups
• The Dedekind \(\sigma\)-completion of a Riesz space
• Order convergence structure onC(X)
• Convergence and Cauchy Structures on Lattice Ordered Groups
• Completion of Pseudo-Topological Vector Spaces

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