| Title:
|
On finite powers of countably compact groups (English) |
| Author:
|
Tomita, Artur Hideyuki |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
617-626 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We will show that under ${M\kern -1.8pt A\kern 0.2pt }_{countable}$ for each $k \in \Bbb N$ there exists a group whose $k$-th power is countably compact but whose $2^k$-th power is not countably compact. In particular, for each $k \in \Bbb N$ there exists $l \in [k,2^k)$ and a group whose $l$-th power is countably compact but the $l+1$-st power is not countably compact. (English) |
| Keyword:
|
countable compactness |
| Keyword:
|
${M\kern -1.8pt A\kern 0.2pt }_{countable}$ |
| Keyword:
|
topological groups |
| Keyword:
|
finite powers |
| MSC:
|
22A05 |
| MSC:
|
54A35 |
| MSC:
|
54B10 |
| MSC:
|
54D20 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 0881.54022 |
| idMR:
|
MR1426926 |
| . |
| Date available:
|
2009-01-08T18:26:37Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118868 |
| . |
| Reference:
|
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| Reference:
|
[2] Comfort W.W.: Problems on topological groups and other homogeneous spaces.Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, 1990, pp. 311-347. MR 1078657 |
| 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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| Reference:
|
[8] Tkachenko M.G.: Countably compact and pseudocompact topologies on free abelian groups.Izvestia VUZ. Matematika 34 (1990), 68-75. Zbl 0714.22001, MR 1083312 |
| Reference:
|
[9] Tomita A.H.: Between countable and sequential compactness in free abelian group.preprint. |
| Reference:
|
[10] Tomita A.H.: A group under $MA_{countable}$ whose square is countably compact but whose cube is not.preprint. |
| Reference:
|
[11] Tomita A.H.: The Wallace Problem: a counterexample from $M A_{countable}$ and $p$-compactness.to appear in Canadian Math. Bulletin. |
| Reference:
|
[12] Weiss W.: Versions of Martin's Axiom.Handbook of Set-Theoretic Topology (K. Kunen and J. Vaughan, eds.), North-Holland, 1984, pp. 827-886. Zbl 0571.54005, MR 0776638 |
| . |
