The order and regular hulls of Riesz spaces
type: Item
instance of: scholarly article
title: The order and regular hulls of Riesz spaces
zbMATH Open document ID: 0878.46003
DOI: 10.1007/BF02104711
published in: Siberian Mathematical Journal
publication date: 1996-08-14T00:00:00Z
review text: We introduce the concept of order hull for a Riesz space (= a vector lattice). This, in particular, makes it possible to exhibit a simple realization of the Dedekind completion of an Archimedean Riesz space. We point out that in similar way the order completion of a Boolean algebra was implemented in [\textit{H. Gonsher}, Lect. Notes Math. 369, 60-70 (1974; Zbl 0276.54045)]. Together with the order hulls, we consider the regular hulls, i.e. the nonstandard hulls of Riesz spaces. The basic method for research in the present article is an embedding of some superstructure \(M\) containing the mathematical objects under study (Riesz spaces, and the like) into the Robinson nonstandard enlargement \({^*M}\). Moreover, we assume the embedding \(M\overset {*} \hookrightarrow{^*M}\) to be polysaturated, which allows us to apply the general saturation principle. The polysaturation assumption can be weakened in each concrete case. However, we refrain from doing so in order to avoid overloading the exposition with unnecessary details.
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46S20
Mathematics Subject Classification ID: 03H05
zbMATH DE Number: 917133
zbMATH Keywords: order hull
zbMATH Keywords: vector lattice
zbMATH Keywords: Dedekind completion
zbMATH Keywords: Archimedean Riesz space
zbMATH Keywords: Boolean algebra
zbMATH Keywords: superstructure
zbMATH Keywords: Robinson nonstandard enlargement
zbMATH Keywords: polysaturation
author: Eduard Yu. Emel'yanov
MaRDI profile type: Publication
cites work: Q4403025
cites work: Q5535809
cites work: Q3283133
cites work: Q5638775
full work available at URL: https://doi.org/10.1007/bf02104711
OpenAlex ID: W2313371853
description: scientific article; zbMATH DE number 917133