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Characterizations of Riesz spaces with b-property

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Abstract

A Riesz space E is said to have b-property if each subset which is order bounded in E~~ is order bounded in E. The relationship between b-property and completeness, being a retract and the absolute weak topology |σ|(E~, 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.

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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey

    Şafak Alpay

  2. Department of Mathematics, Abant İzzet Baysal University, 14280, Bolu, Turkey

    Zafer Ercan

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  1. Şafak Alpay
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  2. Zafer Ercan
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Correspondence to Şafak Alpay.

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Alpay, Ş., Ercan, Z. Characterizations of Riesz spaces with b-property. Positivity 13, 21–30 (2009). https://doi.org/10.1007/s11117-008-2227-6

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  • DOI: https://doi.org/10.1007/s11117-008-2227-6

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