| Title:
|
Descriptive properties of mappings between nonseparable Luzin spaces (English) |
| Author:
|
Holický, Petr |
| Author:
|
Komínek, Václav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
201-224 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We relate some subsets $G$ of the product $X\times Y$ of nonseparable Luzin (e.g., completely metrizable) spaces to subsets $H$ of $\mathbb{N}^{\mathbb{N}}\times Y$ in a way which allows to deduce descriptive properties of $G$ from corresponding theorems on $H$. As consequences we prove a nonseparable version of Kondô’s uniformization theorem and results on sets of points $y$ in $Y$ with particular properties of fibres $f^{-1}(y)$ of a mapping $f\: X\rightarrow Y$. Using these, we get descriptions of bimeasurable mappings between nonseparable Luzin spaces in terms of fibres. (English) |
| Keyword:
|
nonseparable metric spaces |
| Keyword:
|
Luzin spaces |
| Keyword:
|
$\sigma $-discrete network |
| Keyword:
|
uniformization |
| Keyword:
|
bimeasurable maps |
| MSC:
|
28A05 |
| MSC:
|
54E40 |
| MSC:
|
54H05 |
| idZBL:
|
Zbl 1174.54024 |
| idMR:
|
MR2309961 |
| . |
| Date available:
|
2009-09-24T11:45:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128167 |
| . |
| Reference:
|
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| Reference:
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