| Title:
|
Two spaces homeomorphic to $Seq(p)$ (English) |
| Author:
|
Vaughan, Jerry E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
209-218 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the spaces called $Seq(u_t)$, constructed on the set $Seq$ of all finite sequences of natural numbers using ultrafilters $u_t$ to define the topology. For such spaces, we discuss continuity, homogeneity, and rigidity. We prove that $S(u_t)$ is homogeneous if and only if all the ultrafilters $u_t$ have the same Rudin-Keisler type. We proved that a space of Louveau, and in certain cases, a space of Sirota, are homeomorphic to $Seq(p)$ (i.e., $u_t = p$ for all $t\in Seq$). It follows that for a Ramsey ultrafilter $p$, $Seq(p)$ is a topological group. (English) |
| Keyword:
|
ultrafilters |
| Keyword:
|
continuity |
| Keyword:
|
homeomorphisms |
| Keyword:
|
homogeneous |
| Keyword:
|
rigid |
| Keyword:
|
topological group |
| Keyword:
|
Ramsey ultrafilters |
| Keyword:
|
selective ultrafilters |
| MSC:
|
54A35 |
| MSC:
|
54C05 |
| MSC:
|
54D80 |
| MSC:
|
54G05 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1053.54033 |
| idMR:
|
MR1825385 |
| . |
| Date available:
|
2009-01-08T19:09:21Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119236 |
| . |
| Reference:
|
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| . |
