| Title:
|
Extensions of topological and semitopological groups and the product operation (English) |
| Author:
|
Arhangel'skii, A. V. |
| Author:
|
Hušek, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
173-186 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group $G$ that is not Dieudonné complete one can find a Dieudonné complete group $H$ such that the Dieudonné completion of $G\times H$ is not a topological group containing $G\times H$ as a subgroup. Using Korovin's construction of $G_\delta$-dense orbits, we present some examples showing that some results on topological groups are not valid for semitopological groups. (English) |
| Keyword:
|
topological group |
| Keyword:
|
Dieudonné completion |
| Keyword:
|
PT-group |
| Keyword:
|
realcompactness |
| Keyword:
|
\newline Moscow space |
| Keyword:
|
$C$-embedding |
| Keyword:
|
product |
| MSC:
|
22A05 |
| MSC:
|
54B10 |
| MSC:
|
54D35 |
| MSC:
|
54D60 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1053.54043 |
| idMR:
|
MR1825381 |
| . |
| Date available:
|
2009-01-08T19:09:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119232 |
| . |
| Reference:
|
[Ar1] Arhangel'skii A.V.: Functional tightness, $Q$-spaces, and $\tau $-embeddings.Comment. Math. Univ. Carolinae 24:1 (1983), 105-120. MR 0703930 |
| Reference:
|
[Ar2] Arhangel'skii A.V.: Moscow spaces, Pestov-Tkačenko Problem, and $C$-embeddings.Comment. Math. Univ. Carolinae 41:3 (2000), 585-595. Zbl 1038.54013, MR 1795087 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
