Preservation of the Borel class under open-$LC$ functions
Volume 213 / 2011
Fundamenta Mathematicae 213 (2011), 191-195
MSC: Primary 54C10; Secondary 54H05, 54E40, 03E15.
DOI: 10.4064/fm213-2-4
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 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.
