A short proof on lifting of projection properties in Riesz spaces (Q2761026)
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scientific article; zbMATH DE number 1682889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A short proof on lifting of projection properties in Riesz spaces |
scientific article; zbMATH DE number 1682889 |
Statements
17 December 2001
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Dedekind completeness
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spaces of continuous functions
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spaces of Baire functions
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Archimedean Riesz space
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weak order unit
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0.87685126
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0.87052906
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0.8700647
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0.8695076
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0.86912286
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0.8673558
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0.8641199
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A short proof on lifting of projection properties in Riesz spaces (English)
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From author's abstract: Let \(L\) be an Archimedean Riesz space with a weak order unit \(u\). A sufficient condition under which Dedekind [\(\sigma \)-]completeness of the principal ideal \(A_u\) can be lifted to \(L\) is given (Lemma). This yields a concise proof of two theorems of \textit{W. A. J. Luxemburg} and \textit{A. C. Zaanen} concerning projection properties of \(C(X)\)-spaces. Similar results are obtained for the Riesz spaces \(B_{n}(T)\), \(n=1,2,\dots \), of all functions of the \(n\)th Baire class on a metric space \(T\).
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