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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Bibliographic Details
Published inPositivity (Dordrecht) Vol. 7; no. 1-2; pp. 33 - 40
Main Author WNUK, Witold
Format Conference Proceeding Journal Article
LanguageEnglish
Published Heidelberg Springer 01.06.2003
Springer Nature B.V
Subjects
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
United States > US
Order
Topological Riesz space
Vector space
Topological space
Riesz space
Embedding
Regularity
Ordered space
Lattice
Convergence
Lebesgue property
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Summary: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