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A short proof on lifting of projection properties in Riesz spaces

Marek Wójtowicz (1999)

Commentationes Mathematicae Universitatis Carolinae

Let L be an Archimedean Riesz space with a weak order unit u . A sufficient condition under which Dedekind [ σ -]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 , , of all functions of the n th Baire class on a metric space T .

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