| Title:
|
Cellularity of a space of subgroups of a discrete group (English) |
| Author:
|
Leiderman, A. |
| Author:
|
Protasov, I. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
519-522 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a discrete group $G$, we consider the set $\Cal L(G)$ of all subgroups of $G$ endowed with topology of pointwise convergence arising from the standard embedding of $\Cal L(G)$ into the Cantor cube $\{0,1\}^{G}$. We show that the cellularity $c(\Cal L(G))\leq \aleph_0$ for every abelian group $G$, and, for every infinite cardinal $\tau$, we construct a group $G$ with $c(\Cal L(G))=\tau$. (English) |
| Keyword:
|
space of subgroups |
| Keyword:
|
cellularity |
| Keyword:
|
Shanin number |
| MSC:
|
54A25 |
| MSC:
|
54B20 |
| idZBL:
|
Zbl 1212.54100 |
| idMR:
|
MR2490444 |
| . |
| Date available:
|
2009-05-05T17:12:45Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119740 |
| . |
| Reference:
|
[1] Engelking R.: General Topology.PWN, Warszawa, 1985. Zbl 0684.54001 |
| Reference:
|
[2] Protasov I.V.: Dualisms of topological Abelian groups.Ukrain. Mat. Zh. 31 (1979), 207-211; English translation: Ukrainian Math. J. 31 (1979), 164-166. Zbl 0428.22001, MR 0530080, 10.1007/BF01086015 |
| Reference:
|
[3] Protasov I.V.: The Suslin number of a space of subgroups of a locally compact group.Ukrain. Mat. Zh. 40 (1988), 654-658; English translation: Ukrainian Math. J. 40 (1988), 559-562. MR 0971739, 10.1007/BF01057543 |
| Reference:
|
[4] Shanin N.A.: On product of topological spaces.Trudy Mat. Inst. Akad. Nauk SSSR 24 (1948), 1-112 (in Russian). MR 0027310 |
| Reference:
|
[5] Tsybenko Yu.V.: Dyadicity of a space of subgroups of a topological group.Ukrain. Mat. Zh. 38 (1986), 635-639. MR 0870369 |
| Reference:
|
[6] Fuchs L.: Infinite Abelian Groups.Vol. 1, Academic Press, New York and London, 1970. Zbl 0338.20063, MR 0255673 |
| . |
