On regular Riesz subspaces

On regular Riesz subspaces

The paper is devoted to investigations of properties of regular Riesz subspaces and connections between regularity and some topological properties. The problem if a topological closure preserves regularity is solved in the class of discrete Riesz spaces. We also characterize Dedekind complete Riesz...

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Veröffentlicht in:Positivity (Dordrecht) 2003-06, Vol.7 (1-2), p.33-40
1. Verfasser: WNUK, Witold
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Classical statistical mechanics
Convex and discrete geometry
Exact sciences and technology
Geometry
Mathematical models
Mathematics
Number theory
Physics
Sciences and techniques of general use
Statistical physics, thermodynamics, and nonlinear dynamical systems
Studies
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Beschreibung
Zusammenfassung:The paper is devoted to investigations of properties of regular Riesz subspaces and connections between regularity and some topological properties. The problem if a topological closure preserves regularity is solved in the class of discrete Riesz spaces. We also characterize Dedekind complete Riesz spaces possessing the same classes of [sigma]-regular and regular Riesz subspaces Moreover, various examples of regular and non regular Riesz spaces are presented. [PUBLICATION ABSTRACT]
ISSN:1385-1292
1572-9281
DOI:10.1023/A:1025822728628