1. Descriptive properties of mappings between nonseparable Luzin spaces
- Creator:
- Holický, Petr and Komínek, Václav
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- nonseparable metric spaces, Luzin spaces, $\sigma $-discrete network, uniformization, and bimeasurable maps
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public