Geodesic
Preservation of the Borel class under open-$LC$ functions
Alexey Ostrovsky1
1 Helmut-Käutner Str. 25 81739 München, Germany
Fundamenta Mathematicae, Tome 213 (2011) no. 2, pp. 191-195.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $X$ be a Borel subset of the Cantor set $\textbf{C}$ of additive or multiplicative class $\alpha$, and $f: X \to Y $  be a continuous function onto $Y \subset \textbf{C}$ with compact preimages of points. If the image $f(U)$ of every clopen set $U$ is the intersection of an open and a closed set, then $Y$ is a Borel set of the same class $\alpha$. This result generalizes similar results for open and closed functions.
DOI : 10.4064/fm213-2-4
Keywords: borel subset cantor set textbf additive multiplicative class alpha nbsp continuous function subset textbf compact preimages points image every clopen set intersection closed set borel set class alpha result generalizes similar results closed functions

Alexey Ostrovsky 1

1 Helmut-Käutner Str. 25 81739 München, Germany 
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Alexey Ostrovsky. Preservation of  the  Borel class under open-$LC$  functions. Fundamenta Mathematicae, Tome 213 (2011) no. 2, pp. 191-195. doi : 10.4064/fm213-2-4. http://geodesic.mathdoc.fr/articles/10.4064/fm213-2-4/

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