Preservation of the Borel class under open-$LC$ functions

Volume 213 / 2011

Alexey Ostrovsky Fundamenta Mathematicae 213 (2011), 191-195 MSC: Primary 54C10; Secondary 54H05, 54E40, 03E15. DOI: 10.4064/fm213-2-4


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.


  • Alexey OstrovskyHelmut-Käutner Str. 25
    81739 München, Germany

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