Egoroff, $\sigma $, and convergence properties in some archimedean vector lattices

DOI10.4064/sm8363-2-2016zbMath1351.46007OpenAlexW2403386371MaRDI QIDQ2804303

Jan van Mill, Anthony W. Hager

Publication date: 28 April 2016

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/sm8363-2-2016

zbMATH Keywords

Boolean algebraRiesz space\(F\)-spacevector latticeorder convergencealmost \(P\)-spaceEgoroff property\(\sigma\)-propertyrelatively uniform convergencestability of convergence

Mathematics Subject Classification ID

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Stone spaces (Boolean spaces) and related structures (06E15) Lattices of continuous, differentiable or analytic functions (46E05) Ordered topological linear spaces, vector lattices (46A40) Extremally disconnected spaces, (F)-spaces, etc. (54G05) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) (P)-spaces (54G10)

Related Items

Adjoining a strong unit to an Archimedean lattice-ordered group ⋮ Order continuity and regularity on vector lattices and on lattices of continuous functions ⋮ The countable lifting property for Riesz space surjections ⋮ Essential adjunction of a strong unit to an Archimedean lattice-ordered group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• First countability, tightness, and other cardinal invariants in remainders of topological groups
• On the structure of a class of archimedean lattice-ordered algebras
• On the Egoroff Property of Pointwise Convergent Sequences of Functions
• Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions
• On Finitely Additive Measures in Boolean Algebras.
• Extension of continuous functions in 𝛽𝐍
• Seminorms and the Egoroff Property in Riesz Spaces