| Title:
|
Universal meager $F_\sigma$-sets in locally compact manifolds (English) |
| Author:
|
Banakh, Taras |
| Author:
|
Repovš, Dušan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
179-188 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In each manifold $M$ modeled on a finite or infinite dimensional cube $[0,1]^n$, $n\leq \omega $, we construct a meager $F_\sigma$-subset $X\subset M$ which is universal meager in the sense that for each meager subset $A\subset M$ there is a homeomorphism $h:M\to M$ such that $h(A)\subset X$. We also prove that any two universal meager $F_\sigma$-sets in $M$ are ambiently homeomorphic. (English) |
| Keyword:
|
universal nowhere dense subset |
| Keyword:
|
Sierpiński carpet |
| Keyword:
|
Menger cube |
| Keyword:
|
Hilbert cube manifold |
| Keyword:
|
$n$-manifold |
| Keyword:
|
tame ball |
| Keyword:
|
tame decomposition |
| MSC:
|
54F65 |
| MSC:
|
57N20 |
| MSC:
|
57N45 |
| idZBL:
|
Zbl 06221261 |
| idMR:
|
MR3067702 |
| . |
| Date available:
|
2013-06-25T12:48:42Z |
| Last updated:
|
2015-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143268 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Banakh T., Repovš D.: Universal nowhere dense subsets of locally compact manifolds.preprint (http://arxiv.org/abs/1302.5651). |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
