Relative uniform convergence and Archimedean property in pre-ordered vector spaces and abelian groups

2026/02/28 by Eduard Emelyanov
Mathematics · #math.FA #msc:06F20 #msc:46A40 #msc:47B60 #msc:47B65

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arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

It is proved that, for a pre-ordered vector space X, the quotient space (X/A,[W]) is an Archimedeanization of X, where W is the closure of positive wedge X₊ in ru-topology, A=W∩-W, and [W] is the quotient set of W in X/A. A construction of an almost Archimedeanization of a pre-ordered vector space is given. Analogous results are presented for pre-ordered groups.

Citations

• Relatively uniformly continuous semigroups on ordered vector spaces
• Collective order boundedness of sets of operators between ordered vector spaces
• Free and Projective Banach Lattices
• Vector spaces with an order unit

Related

• Note on Archimedean property in ordered vector spaces
• Archimedeanization of ordered vector spaces
• The four uniform completions of a unital archimedean vector lattice
• The Archimedean order unitization of seminormed ordered vector spaces
• Atomicity of Boolean algebras and vector lattices in terms of order convergence