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

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 $Y\subset \text{C}.$ 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.

5 pages