Borel sets with σ-compact sections for nonseparable spaces

• Autorzy: Petr Holický
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54C65: Selections
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 199
• Numer: 2
• Strony: 139-154

Daty

wydano

2008

Twórcy

autor

Petr Holický

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/fm199-2-4