| Title:
|
Locally minimal topological groups and their embeddings into products of $o$-bounded groups (English) |
| Author:
|
Banakh, T. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
811-815 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proven that an infinite-dimensional Banach space (considered as an Abelian topological group) is not topologically isomorphic to a subgroup of a product of $\sigma $-compact (or more generally, $o$-bounded) topological groups. This answers a question of M. Tkachenko. (English) |
| Keyword:
|
$\omega$-bounded group |
| Keyword:
|
$\sigma$-bounded group |
| Keyword:
|
$o$-bounded group |
| Keyword:
|
Weil complete group |
| Keyword:
|
locally minimal group |
| Keyword:
|
Lie group |
| MSC:
|
22A05 |
| MSC:
|
22E15 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1049.54034 |
| idMR:
|
MR1800163 |
| . |
| Date available:
|
2009-01-08T19:07:34Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119212 |
| . |
| Reference:
|
Gleason A.M.: Groups without small subgroups.Ann. Math. (1952), 56 193-212. Zbl 0049.30105, MR 0049203 |
| Reference:
|
Guran I.: On topological groups close to being Lindelöf.Soviet Math. Dokl. 23 (1981), 173-175. Zbl 0478.22002 |
| Reference:
|
Hernández C.: Topological groups close to being $\sigma$-compact.Topology Appl. 102 (2000), 101-111. MR 1739266 |
| Reference:
|
Montgomery D., Zippin L.: Topological transformation groups.Interscience N.Y. (1955). Zbl 0068.01904, MR 0073104 |
| Reference:
|
Tkachenko M.: Introduction to topological groups.Topology Appl. (1998), 86 179-231. Zbl 0955.54013, MR 1623960 |
| . |
