| Title:
|
Topologies on groups determined by right cancellable ultrafilters (English) |
| Author:
|
Protasov, I. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
135-139 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For every discrete group $G$, the Stone-Čech compactification $\beta G$ of $G$ has a natural structure of a compact right topological semigroup. An ultrafilter $p\in G^*$, where $G^*=\beta G\setminus G$, is called right cancellable if, given any $q,r\in G^*$, $qp=rp$ implies $q=r$. For every right cancellable ultrafilter $p\in G^*$, we denote by $G(p)$ the group $G$ endowed with the strongest left invariant topology in which $p$ converges to the identity of $G$. For any countable group $G$ and any right cancellable ultrafilters $p,q\in G^*$, we show that $G(p)$ is homeomorphic to $G(q)$ if and only if $p$ and $q$ are of the same type. (English) |
| Keyword:
|
Stone-Čech compactification |
| Keyword:
|
right cancellable ultrafilters |
| Keyword:
|
left invariant topologies |
| MSC:
|
54C05 |
| MSC:
|
54G15 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1212.54101 |
| idMR:
|
MR2562810 |
| . |
| Date available:
|
2009-08-18T12:23:47Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133421 |
| . |
| Reference:
|
[1] Hindman N., Strauss D.: Algebra in the Stone-Čech Compactification: Theory and Applications.Walter de Gruyter, Berlin, 1998. Zbl 0918.22001, MR 1642231 |
| Reference:
|
[2] Hindman N., Protasov I., Strauss D.: Topologies on $S$ determined by idempotents in $\beta S$.Topology Proc. 23 (1998), 155--190. Zbl 0970.54036, MR 1803247 |
| Reference:
|
[3] Protasov I.V.: Maximal topologies on groups.Siberian Math. J. 39 (1998), 1184--1194. Zbl 0935.22002, MR 1672661, 10.1007/BF02674129 |
| Reference:
|
[4] Protasov I.V.: Extremal topologies on groups.Mat. Stud. 15 (2001), 9--22. Zbl 0989.22003, MR 1871923 |
| Reference:
|
[5] Protasov I.V.: Remarks on extremally disconnected semitopological groups.Comment. Math. Univ. Carolin. 43 (2002), 343--347. Zbl 1090.54033, MR 1922132 |
| Reference:
|
[6] Vaughan J.E.: Two spaces homeomorphic to $Seq(p)$.Comment. Math. Univ. Carolin. 42 (2001), 209--218. Zbl 1053.54033, MR 1825385 |
| . |
