| Title:
|
Diagonals of separately continuous functions of $n$ variables with values in strongly $\sigma$-metrizable spaces (English) |
| Author:
|
Karlova, Olena |
| Author:
|
Mykhaylyuk, Volodymyr |
| Author:
|
Sobchuk, Oleksandr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
103-122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the result on Baire classification of mappings $f:X\times Y\to Z$ which are continuous with respect to the first variable and belongs to a Baire class with respect to the second one, where $X$ is a $PP$-space, $Y$ is a topological space and $Z$ is a strongly $\sigma$-metrizable space with additional properties. We show that for any topological space $X$, special equiconnected space $Z$ and a mapping $g:X\to Z$ of the $(n-1)$-th Baire class there exists a strongly separately continuous mapping $f:X^n\to Z$ with the diagonal $g$. For wide classes of spaces $X$ and $Z$ we prove that diagonals of separately continuous mappings $f:X^n\to Z$ are exactly the functions of the $(n-1)$-th Baire class. An example of equiconnected space $Z$ and a Baire-one mapping $g:[0,1]\to Z$, which is not a diagonal of any separately continuous mapping $f:[0,1]^2\to Z$, is constructed. (English) |
| Keyword:
|
diagonal of a mapping |
| Keyword:
|
separately continuous mapping |
| Keyword:
|
Baire-one mapping |
| Keyword:
|
equiconnected space |
| Keyword:
|
strongly $\sigma$-metrizable space |
| MSC:
|
26B05 |
| MSC:
|
54C05 |
| MSC:
|
54C08 |
| idZBL:
|
Zbl 06562201 |
| idMR:
|
MR3478344 |
| DOI:
|
10.14712/1213-7243.2015.152 |
| . |
| Date available:
|
2016-04-12T05:09:10Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144920 |
| . |
| Reference:
|
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