Characterizations of Riesz spaces with b-property |
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| Authors: | ?afak Alpay Zafer Ercan |
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| Institution: | (1) Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey;(2) Department of Mathematics, Abant İzzet Baysal University, 14280 Bolu, Turkey |
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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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| Keywords: | Riesz spaces b-property locally solid Riesz spaces Levi property |
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