关于FSIN群的Itzkowitz问题的解答
The answer about Itzkowitz's Problems on FSIN groups
- Institute of Mathematics, Nanjing Normal University（南京师范大学数学系）
- School of Mathematics and Computational Science, Wuyi University（五邑大学数学与计算科学学院）
- School of Mathematical Sciences, Guangxi Minzu University（广西民族大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明每个Hausdorff函数平衡群的左右一致性相同，肯定回答了Itzkowitz问题，从而得出SIN、SFSIN和FSIN群类一致。
AI中文摘要：
一个拓扑群被称为函数平衡的，如果每个有界实值左一致连续函数都是右一致连续的。我们证明了每个Hausdorff函数平衡群具有相同的左一致性和右一致性，从而对Itzkowitz问题给出了肯定回答。因此，SIN、SFSIN和FSIN群这三类群是一致的。
英文摘要：
A topological group is functionally balanced if every bounded real-valued left uniformly continuous function is right uniformly continuous. We prove that every Hausdorff functionally balanced group has coinciding left and right uniformities, giving an affirmative answer to the Itzkowitz problem. Consequently, the classes of SIN, SFSIN and FSIN groups coincide.
