Preservation of the Borel class under open-$LC$ functions
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.
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
Affiliations des auteurs :
Alexey Ostrovsky 1
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author = {Alexey Ostrovsky},
title = {Preservation of the {Borel} class under open-$LC$ functions},
journal = {Fundamenta Mathematicae},
pages = {191--195},
publisher = {mathdoc},
volume = {213},
number = {2},
year = {2011},
doi = {10.4064/fm213-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm213-2-4/}
}
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
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