- Tytuł:
- A converse of the Arsenin–Kunugui theorem on Borel sets with σ-compact sections
- Autorzy:
-
Holický, P.
Zelený, Miroslav - Powiązania:
- https://bibliotekanauki.pl/articles/1205005.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
$K_σ$ sections
Borel bimeasurability - Opis:
- Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel metric) space L onto a metric space M such that f(F) is a Borel subset of M if F is closed in L. We show that then $f^{-1}(y)$ is a $K_σ$ set for all except countably many y ∈ M, that M is also Luzin, and that the Borel classes of the sets f(F), F closed in L, are bounded by a fixed countable ordinal. This gives a converse of the classical theorem of Arsenin and Kunugui. As a particular case we get Taĭmanov's theorem saying that the image of a Luzin space under a closed continuous mapping is a Luzin space. The method is based on a parametrized version of a Hurewicz type theorem and on the use of the Jankov-von Neumann selection theorem.
- Źródło:
-
Fundamenta Mathematicae; 2000, 165, 3; 191-202
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł