A short proof on lifting of projection properties in Riesz spaces

Wójtowicz, Marek. "A short proof on lifting of projection properties in Riesz spaces." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 277-278. <http://eudml.org/doc/248399>.

@article{Wójtowicz1999,
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 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 $T$.},
author = {Wójtowicz, Marek},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Dedekind completeness; spaces of continuous functions; spaces of Baire functions; Dedekind completeness; spaces of continuous functions; spaces of Baire functions; Archimedean Riesz space; weak order unit},
language = {eng},
number = {2},
pages = {277-278},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A short proof on lifting of projection properties in Riesz spaces},
url = {http://eudml.org/doc/248399},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Wójtowicz, Marek
TI - A short proof on lifting of projection properties in Riesz spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 277
EP - 278
AB - 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 $T$.
LA - eng
KW - Dedekind completeness; spaces of continuous functions; spaces of Baire functions; Dedekind completeness; spaces of continuous functions; spaces of Baire functions; Archimedean Riesz space; weak order unit
UR - http://eudml.org/doc/248399
ER -