# Diagonals of separately continuous functions of $n$ variables with values in strongly $\sigma $-metrizable spaces

Olena Karlova; Volodymyr Mykhaylyuk; Oleksandr Sobchuk

Commentationes Mathematicae Universitatis Carolinae (2016)

- Volume: 57, Issue: 1, page 103-122
- ISSN: 0010-2628

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topKarlova, Olena, Mykhaylyuk, Volodymyr, and Sobchuk, Oleksandr. "Diagonals of separately continuous functions of $n$ variables with values in strongly $\sigma $-metrizable spaces." Commentationes Mathematicae Universitatis Carolinae 57.1 (2016): 103-122. <http://eudml.org/doc/276820>.

@article{Karlova2016,

abstract = {We prove the result on Baire classification of mappings $f:X\times Y\rightarrow Z$ 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 $g:X\rightarrow Z$ of the $(n-1)$-th Baire class there exists a strongly separately continuous mapping $f:X^n\rightarrow Z$ with the diagonal $g$. For wide classes of spaces $X$ and $Z$ we prove that diagonals of separately continuous mappings $f:X^n\rightarrow Z$ are exactly the functions of the $(n-1)$-th Baire class. An example of equiconnected space $Z$ and a Baire-one mapping $g:[0,1]\rightarrow Z$, which is not a diagonal of any separately continuous mapping $f:[0,1]^2\rightarrow Z$, is constructed.},

author = {Karlova, Olena, Mykhaylyuk, Volodymyr, Sobchuk, Oleksandr},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {diagonal of a mapping; separately continuous mapping; Baire-one mapping; equiconnected space; strongly $\sigma $-metrizable space},

language = {eng},

number = {1},

pages = {103-122},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Diagonals of separately continuous functions of $n$ variables with values in strongly $\sigma $-metrizable spaces},

url = {http://eudml.org/doc/276820},

volume = {57},

year = {2016},

}

TY - JOUR

AU - Karlova, Olena

AU - Mykhaylyuk, Volodymyr

AU - Sobchuk, Oleksandr

TI - Diagonals of separately continuous functions of $n$ variables with values in strongly $\sigma $-metrizable spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2016

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 57

IS - 1

SP - 103

EP - 122

AB - We prove the result on Baire classification of mappings $f:X\times Y\rightarrow Z$ 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 $g:X\rightarrow Z$ of the $(n-1)$-th Baire class there exists a strongly separately continuous mapping $f:X^n\rightarrow Z$ with the diagonal $g$. For wide classes of spaces $X$ and $Z$ we prove that diagonals of separately continuous mappings $f:X^n\rightarrow Z$ are exactly the functions of the $(n-1)$-th Baire class. An example of equiconnected space $Z$ and a Baire-one mapping $g:[0,1]\rightarrow Z$, which is not a diagonal of any separately continuous mapping $f:[0,1]^2\rightarrow Z$, is constructed.

LA - eng

KW - diagonal of a mapping; separately continuous mapping; Baire-one mapping; equiconnected space; strongly $\sigma $-metrizable space

UR - http://eudml.org/doc/276820

ER -

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