Borel sets with σ-compact sections for nonseparable spaces

Petr Holický. "Borel sets with σ-compact sections for nonseparable spaces." Fundamenta Mathematicae 199.2 (2008): 139-154. <http://eudml.org/doc/283199>.

@article{PetrHolický2008,
abstract = {We prove that every (extended) Borel subset E of X × Y, where X is complete metric and Y is Polish, can be covered by countably many extended Borel sets with compact sections if the sections $E_x = \{y ∈ Y: (x,y) ∈ E\}$, x ∈ X, are σ-compact. This is a nonseparable version of a theorem of Saint Raymond. As a by-product, we get a proof of Saint Raymond’s result which does not use transfinite induction.},
author = {Petr Holický},
journal = {Fundamenta Mathematicae},
keywords = {extended Borel sets; -compact sections; nonseparable metric spaces},
language = {eng},
number = {2},
pages = {139-154},
title = {Borel sets with σ-compact sections for nonseparable spaces},
url = {http://eudml.org/doc/283199},
volume = {199},
year = {2008},
}

TY - JOUR
AU - Petr Holický
TI - Borel sets with σ-compact sections for nonseparable spaces
JO - Fundamenta Mathematicae
PY - 2008
VL - 199
IS - 2
SP - 139
EP - 154
AB - We prove that every (extended) Borel subset E of X × Y, where X is complete metric and Y is Polish, can be covered by countably many extended Borel sets with compact sections if the sections $E_x = {y ∈ Y: (x,y) ∈ E}$, x ∈ X, are σ-compact. This is a nonseparable version of a theorem of Saint Raymond. As a by-product, we get a proof of Saint Raymond’s result which does not use transfinite induction.
LA - eng
KW - extended Borel sets; -compact sections; nonseparable metric spaces
UR - http://eudml.org/doc/283199
ER -