| Title:
|
On the complexity of some $\sigma$-ideals of $\sigma$-P-porous sets (English) |
| Author:
|
Zajíček, Luděk |
| Author:
|
Zelený, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
531-554 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\bold P$ be a porosity-like relation on a separable locally compact metric space $E$. We show that the $\sigma$-ideal of compact $\sigma$-$\bold P$-porous subsets of $E$ (under some general conditions on $\bold P$ and $E$) forms a $\boldsymbol \Pi_{\bold 1}^{\bold 1}$-complete set in the hyperspace of all compact subsets of $E$, in particular it is coanalytic and non-Borel. Our general results are applicable to most interesting types of porosity. It is shown in the cases of the $\sigma$-ideals of $\sigma$-porous sets, $\sigma$-$\langle g \rangle$-porous sets, $\sigma$-strongly porous sets, $\sigma$-symmetrically porous sets and $\sigma$-strongly symmetrically porous sets. We prove a similar result also for $\sigma$-very porous sets assuming that each singleton of $E$ is very porous set. (English) |
| Keyword:
|
$\sigma $-porous sets |
| Keyword:
|
$\sigma $-ideal |
| Keyword:
|
coanalytic sets |
| Keyword:
|
Hausdorff metric |
| MSC:
|
28A05 |
| MSC:
|
54H05 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1099.54029 |
| idMR:
|
MR2025819 |
| . |
| Date available:
|
2009-01-08T19:30:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119407 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| . |
