| Title:
|
Covering $^\omega\omega$ by special Cantor sets (English) |
| Author:
|
Gruenhage, Gary |
| Author:
|
Levy, Ronnie |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
497-509 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space $^\omega \omega $ of irrationals, or certain of its subspaces. In particular, given $f\in {}^\omega (\omega \setminus \{0\})$, we consider compact sets of the form $\prod_{i\in \omega }B_i$, where $|B_i|= f(i)$ for all, or for infinitely many, $i$. We also consider ``$n$-splitting'' compact sets, i.e., compact sets $K$ such that for any $f\in K$ and $i\in \omega $, $|\{g(i):g\in K, g\restriction i=f\restriction i\}|= n$. (English) |
| Keyword:
|
irrationals |
| Keyword:
|
$f$-cone |
| Keyword:
|
weak $f$-cone |
| Keyword:
|
$n$-splitting compact set |
| MSC:
|
03E17 |
| MSC:
|
03E35 |
| MSC:
|
54A35 |
| idZBL:
|
Zbl 1072.03028 |
| idMR:
|
MR1920525 |
| . |
| Date available:
|
2009-01-08T19:24:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119339 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/119446 |
| . |
| Reference:
|
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| . |
