Borel类在开$LC$函数下的保持性
Preservation of the Borel class under open-$LC$ functions
摘要：
设$X$是加法类或乘法类$α,$的Cantor集\textbf{C}的Borel子集，$f: X \to Y$是点在$Y \subset \textbf{C}.$上具有紧原像的连续函数，若每个闭集$U$的像$f(U)$是开集与闭集的交，则$Y$是同一类的Borel集.这一结果推广了开函数和闭函数的类似结果。
英文摘要：
Let $X$ be a Borel subset of the Cantor set \textbf{C} of additive or multiplicative class $α,$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
