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arXiv · 1102.3253

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

Alexey Ostrovsky
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Abstract

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 with compact preimages of points onto $Y \subset \textbf{C}.$ 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. This result generalizes similar results for open and closed functions.

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Alexey Ostrovsky. 2011-02-16. Preservation of the Borel class under open-$LC$ functions. https://arxiv.org/abs/1102.3253

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