| Title:
|
On $\omega$-resolvable and almost-$\omega$-resolvable spaces (English) |
| Author:
|
Angoa, J. |
| Author:
|
Ibarra, M. |
| Author:
|
Tamariz-Mascarúa, A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
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49 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
485-508 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We continue the study of almost-$\omega$-resolvable spaces beginning in A. Tamariz-Mascar'ua, H. Villegas-Rodr'{\i}guez, {\it Spaces of continuous functions, box products and almost-$\omega$-resoluble spaces\/}, Comment. Math. Univ. Carolin. {\bf 43} (2002), no. 4, 687--705. We prove in ZFC: (1) every crowded $T_0$ space with countable tightness and every $T_1$ space with $\pi$-weight $\leq \aleph _1$ is hereditarily almost-$\omega$-resolvable, (2) every crowded paracompact $T_2$ space which is the closed preimage of a crowded Fréchet $T_2$ space in such a way that the crowded part of each fiber is $\omega$-resolvable, has this property too, and (3) every Baire dense-hereditarily almost-$\omega$-resolvable space is $\omega$-resolvable. Moreover, by using the concept of almost-$\omega$-resolvability, we obtain two results due the first one to O. Pavlov and the other to V.I. Malykhin: (1) $V = L$ implies that every crowded Baire space is $\omega$-resolvable, and (2) $V = L$ implies that the product of two crowded spaces is resolvable. Finally, we prove that the product of two almost resolvable spaces is resolvable. (English) |
| Keyword:
|
Baire spaces |
| Keyword:
|
resolvable spaces |
| Keyword:
|
almost resolvable spaces |
| Keyword:
|
almost-$\omega$-resolvable spaces |
| Keyword:
|
tightness |
| Keyword:
|
$\pi$-weight |
| MSC:
|
54A10 |
| MSC:
|
54A35 |
| MSC:
|
54C05 |
| MSC:
|
54D10 |
| MSC:
|
54E52 |
| idZBL:
|
Zbl 1212.54069 |
| idMR:
|
MR2490442 |
| . |
| Date available:
|
2009-05-05T17:12:35Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119738 |
| . |
| Reference:
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