# A short proof on lifting of projection properties in Riesz spaces

Commentationes Mathematicae Universitatis Carolinae (1999)

- Volume: 40, Issue: 2, page 277-278
- ISSN: 0010-2628

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topWójtowicz, 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 -

## References

top- Kuratowski K., Introduction to Set Theory and Topology, Polish Scientific Publishers, Warszawa, 1997. Zbl1081.54501MR0346724
- Kuratowski K., Mostowski A., Set Theory, Polish Scientific Publishers, Warszawa, 1996. Zbl0337.02034MR0485384
- Luxemburg W.A.J., Zaanen A.C., Riesz Spaces I, North-Holland, Amsterdam, 1971.

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