有限指数群的Itzkowitz问题
Itzkowitz's problem for group of finite exponent
摘要：
Itzkowitz的问题是，如果$G$上的有界左一致连续实值函数是右一致连续的，那么是否每个拓扑群$G$都有相等的左、右一致结构.本文给出了这个问题的一个肯定答案，如果$G$是有界指数的，或者更一般地，如果存在一个整数$p\geq 2$和一个非空开集$U\subset G$，使得幂映射$U\ni g\to g^p\in G$是左（或右）一致连续的.这也解决了问题的周期群是Baire空间。
英文摘要：
Itzkowitz's problem asks whether every topological group $G$ has equal left and right uniform structures provided that bounded left uniformly continuous real-valued function on $G$ are right uniformly continuous. This paper provides a positive answer to this problem if $G$ is of bounded exponent or, more generally, if there exist an integer $p\geq 2$ and a nonempty open set $U\subset G$ such that the power map $U\ni g\to g^p\in G$ is left (or right) uniformly continuous. This also resolves the problem for periodic groups which are Baire spaces.
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。
