Characterizations of Riesz spaces with b-property

Alpay S., ERCAN Z.

POSITIVITY, vol.13, no.1, pp.21-30, 2009 (SCI-Expanded) identifier identifier

  • 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.