| Title:
|
On zero-dimensionality of subgroups of locally compact groups (English) |
| Author:
|
Shakhmatov, Dmitrii B. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
581-582 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Improving the recent result of the author we show that $\operatorname{ind}H=0$ is equivalent to $\operatorname{dim} H=0$ for every subgroup $H$ of a Hausdorff locally compact group $G$. (English) |
| Keyword:
|
zero-dimensionality |
| Keyword:
|
covering dimension |
| Keyword:
|
inductive dimension |
| Keyword:
|
subgroup |
| Keyword:
|
locally compact group |
| MSC:
|
22A05 |
| MSC:
|
22D05 |
| MSC:
|
54D45 |
| MSC:
|
54F45 |
| MSC:
|
54H11 |
| MSC:
|
54H99 |
| idZBL:
|
Zbl 0746.22004 |
| idMR:
|
MR1159803 |
| . |
| Date available:
|
2009-01-08T17:47:08Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118435 |
| . |
| Reference:
|
[1] Engelking R.: General Topology.Warszawa, PWN, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[2] Hewitt E., Ross K.A.: Abstract Harmonic Analysis, vol. 1. Structure of Topological Groups. Integration Theory. Group Representations.Die Grundlehren der mathematischen Wissenshaften, Bd. 115, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. Zbl 0416.43001, MR 0156915 |
| Reference:
|
[3] Shakhmatov D.B.: Imbeddings into topological groups preserving dimensions.Topology Appl. 36 (1990), 181-204. Zbl 0709.22001, MR 1068169 |
| Reference:
|
[4] Tkačenko M.G.: Factorization theorems for topological groups and their applications.Topology Appl. 38 (1991), 21-37. MR 1093863 |
| . |
