| Title:
|
Homomorphic images of $\Bbb R$-factorizable groups (English) |
| Author:
|
Tkachenko, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
525-537 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well known that every $\Bbb R$-factorizable group is $\omega $-narrow, but not vice versa. One of the main problems regarding $\Bbb R$-factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every $\omega $-narrow group is a continuous homomorphic image of an $\Bbb R$-factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an $\Bbb R$-factorizable group is a $P$-group, then the image is also $\Bbb R$-factorizable. (English) |
| Keyword:
|
$\Bbb R$-factorizable |
| Keyword:
|
totally bounded |
| Keyword:
|
$\omega $-narrow |
| Keyword:
|
complete |
| Keyword:
|
Lindelöf |
| Keyword:
|
$P$-space |
| Keyword:
|
realcompact |
| Keyword:
|
Dieudonné-complete |
| Keyword:
|
pseudo-$\omega _1$-compact |
| MSC:
|
22A05 |
| MSC:
|
54C10 |
| MSC:
|
54C45 |
| MSC:
|
54D20 |
| MSC:
|
54D60 |
| MSC:
|
54G10 |
| MSC:
|
54G20 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1150.54035 |
| idMR:
|
MR2281014 |
| . |
| Date available:
|
2009-05-05T16:59:17Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119613 |
| . |
| Reference:
|
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| . |
