| Title:
|
Subgroups and products of $\Bbb R$-factorizable $P$-groups (English) |
| Author:
|
Hernández, Constancio |
| Author:
|
Tkachenko, Michael |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
153-167 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that {\it every\/} subgroup of an $\Bbb R$-factorizable abelian $P$-group is topologically isomorphic to a {\it closed\/} subgroup of another $\Bbb R$-factorizable abelian $P$-group. This implies that closed subgroups of $\Bbb R$-factorizable $P$-groups are not necessarily $\Bbb R$-factorizable. We also prove that if a Hausdorff space $Y$ of countable pseudocharacter is a continuous image of a product $X=\prod_{i\in I}X_i$ of $P$-spaces and the space $X$ is pseudo-$\omega _1$-compact, then $nw(Y)\leq \aleph_0$. In particular, direct products of $\Bbb R$-factorizable $P$-groups are $\Bbb R$-factorizable and $\omega $-stable. (English) |
| Keyword:
|
$P$-space |
| Keyword:
|
$P$-group |
| Keyword:
|
pseudo-$\omega _1$-compact |
| Keyword:
|
$\omega $-stable |
| Keyword:
|
$\Bbb R$-factorizable |
| Keyword:
|
$\aleph _0$-bounded |
| Keyword:
|
pseudocharacter |
| Keyword:
|
cellularity |
| Keyword:
|
$\aleph_ 0$-box topology |
| Keyword:
|
$\sigma $-product |
| MSC:
|
22A05 |
| MSC:
|
54A25 |
| MSC:
|
54C10 |
| MSC:
|
54C25 |
| MSC:
|
54G10 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1100.54026 |
| idMR:
|
MR2076867 |
| . |
| Date available:
|
2009-05-05T16:44:01Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119444 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
