| Title:
|
A short proof on lifting of projection properties in Riesz spaces (English) |
| Author:
|
Wójtowicz, Marek |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
277-278 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $T$. (English) |
| Keyword:
|
Dedekind completeness |
| Keyword:
|
spaces of continuous functions |
| Keyword:
|
spaces of Baire functions |
| MSC:
|
26A99 |
| MSC:
|
46A40 |
| MSC:
|
46B30 |
| MSC:
|
46B40 |
| MSC:
|
46E05 |
| idZBL:
|
Zbl 0983.46006 |
| idMR:
|
MR1732648 |
| . |
| Date available:
|
2009-01-08T18:52:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119083 |
| . |
| Reference:
|
[1] Kuratowski K.: Introduction to Set Theory and Topology.Polish Scientific Publishers, Warszawa, 1997. Zbl 1081.54501, MR 0346724 |
| Reference:
|
[2] Kuratowski K., Mostowski A.: Set Theory.Polish Scientific Publishers, Warszawa, 1996. Zbl 0337.02034, MR 0485384 |
| Reference:
|
[3] Luxemburg W.A.J., Zaanen A.C.: Riesz Spaces I.North-Holland, Amsterdam, 1971. |
| . |
