| Title:
|
The existence of initially $\omega_1$-compact group topologies on free Abelian groups is independent of ZFC (English) |
| Author:
|
Tomita, Artur Hideyuki |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
401-413 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It was known that free Abelian groups do not admit a Hausdorff compact group topology. Tkachenko showed in 1990 that, under CH, a free Abelian group of size ${\frak C}$ admits a Hausdorff countably compact group topology. We show that no Hausdorff group topology on a free Abelian group makes its $\omega$-th power countably compact. In particular, a free Abelian group does not admit a Hausdorff $p$-compact nor a sequentially compact group topology. Under CH, we show that a free Abelian group does not admit a Hausdorff initially $\omega_1$-compact group topology. We also show that the existence of such a group topology is independent of ${\frak C} = \aleph_2$. (English) |
| Keyword:
|
free Abelian group |
| Keyword:
|
countable compactness |
| Keyword:
|
products |
| Keyword:
|
initially $\omega_1$-compact |
| Keyword:
|
Martin's Axiom |
| MSC:
|
22B99 |
| MSC:
|
54D30 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 0938.54034 |
| idMR:
|
MR1651991 |
| . |
| Date available:
|
2009-01-08T18:41:30Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119017 |
| . |
| Reference:
|
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| Reference:
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