| Title:
|
Complete $\aleph_0$-bounded groups need not be $\Bbb R$-factorizable (English) |
| Author:
|
Tkachenko, M. G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
551-559 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present an example of a complete $\aleph_0$-bounded topological group $H$ which is not $\Bbb R$-factorizable. In addition, every $G_\delta$-set in the group $H$ is open, but $H$ is not Lindelöf. (English) |
| Keyword:
|
$\Bbb R$-factorizable group |
| Keyword:
|
$\aleph_0$-bounded group |
| Keyword:
|
$P$-group |
| Keyword:
|
complete |
| Keyword:
|
Lindelöf |
| MSC:
|
22A05 |
| MSC:
|
54D20 |
| MSC:
|
54G10 |
| MSC:
|
54G20 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1053.54045 |
| idMR:
|
MR1860244 |
| . |
| Date available:
|
2009-01-08T19:16:06Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119270 |
| . |
| Reference:
|
[1] Guran I.: On topological groups close to being Lindelöf.Soviet Math. Dokl. 23 (1981), 173-175. Zbl 0478.22002 |
| Reference:
|
[2] Jech T.: Lectures in set theory.Lectures Notes in Math. 217, Berlin, 1971. Zbl 0269.02030 |
| Reference:
|
[3] Tkachenko M.G.: Generalization of a theorem of Comfort and Ross.Ukrainian Math. J. 41 (1989), 334-338; Russian original in Ukrain. Mat. Zh. 41 (1989), 377-382. MR 1001546 |
| Reference:
|
[4] Tkachenko M.G.: Subgroups, quotient groups and products of $\Bbb R$-factorizable groups.Topology Proc. 16 (1991), 201-231. MR 1206464 |
| Reference:
|
[5] Tkachenko M.G.: Factorization theorems for topological groups and their applications.Topology Appl. 38 (1991), 21-37. Zbl 0722.54039, MR 1093863 |
| Reference:
|
[6] Tkachenko M.G.: Introduction to topological groups.Topology Appl. 86 (1998), 179-231. Zbl 0955.54013, MR 1623960 |
| Reference:
|
[7] Williams S.W.: Box products.in Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan, eds., Chapter 4, North-Holland, Amsterdam, 1984, pp.169-200. Zbl 0769.54008, MR 0776623 |
| . |
