Geodesic
Descriptive properties of mappings between nonseparable Luzin spaces
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 201-224 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 28A05, 54E40, 54H05
Keywords: nonseparable metric spaces; Luzin spaces; $\sigma $-discrete network; uniformization; bimeasurable maps 
@article{CMJ_2007_57_1_a17,
     author = {Holick\'y, Petr and Kom{\'\i}nek, V\'aclav},
     title = {Descriptive properties of mappings between nonseparable {Luzin} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {201--224},
     year = {2007},
     volume = {57},
     number = {1},
     mrnumber = {2309961},
     zbl = {1174.54024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a17/}
}
TY  - JOUR
AU  - Holický, Petr
AU  - Komínek, Václav
TI  - Descriptive properties of mappings between nonseparable Luzin spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 201
EP  - 224
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a17/
LA  - en
ID  - CMJ_2007_57_1_a17
ER  - 
%0 Journal Article
%A Holický, Petr
%A Komínek, Václav
%T Descriptive properties of mappings between nonseparable Luzin spaces
%J Czechoslovak Mathematical Journal
%D 2007
%P 201-224
%V 57
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a17/
%G en
%F CMJ_2007_57_1_a17
Holický, Petr; Komínek, Václav. Descriptive properties of mappings between nonseparable Luzin spaces. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 201-224. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a17/