Geodesic
Descriptive properties of mappings between nonseparable Luzin spaces
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 201-224.

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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 
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     title = {Descriptive properties of mappings between nonseparable {Luzin} spaces},
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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/