Characterizations of Riesz spaces with b-property
POSITIVITY, vol.13, no.1, pp.21-30, 2009 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 13 Issue: 1
- Publication Date: 2009
- Doi Number: 10.1007/s11117-008-2227-6
- Journal Name: POSITIVITY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.21-30
- Keywords: Riesz spaces, b-property, locally solid Riesz spaces, Levi property
- Middle East Technical University Affiliated: Yes
Abstract
A Riesz space E is said to have b-property if each subset which is order bounded in E(similar to similar to) is order bounded in E. The relationship between b-property and completeness, being a retract and the absolute weak topology vertical bar sigma vertical bar (E(similar to), E) is studied. Perfect Riesz spaces are characterized in terms of b-property. It is shown that b-property coincides with the Levi property in Dedekind complete Frechet lattices.