Geodesic
A short proof on lifting of projection properties in Riesz spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 277-278.

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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 Luxemburg and 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 $T$.
Classification : 26A99, 46A40, 46B30, 46B40, 46E05
Keywords: Dedekind completeness; spaces of continuous functions; spaces of Baire functions 
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Wójtowicz, Marek. A short proof on lifting of projection properties in Riesz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 277-278. http://geodesic.mathdoc.fr/item/CMUC_1999__40_2_a8/