关于generalized characters的一个注记
A note on generalized characters
摘要：
对于紧生成的LCA群$G$，证明了$G$上所有广义特征标的集合$H(G)$是LCA群，且$H(G) = \dg$（$G$的对偶群）当且仅当$G$是紧的.这两个结果失败的任意LCA组。进一步地，如果$G$是第二可数的，则具有归纳极限拓扑的交换卷积代数$\ccg$的Gel'fand空间与$\hg$拓扑同胚.
英文摘要：
For a compactly generated LCA group $G$, it is shown that the set $H(G)$ of all generalized characters on $G$ equipped with the compact-open topology is a LCA group and $H(G) = \dg$ (the dual group of $G$) if and only if $G$ is compact. Both results fail for arbitrary LCA groups. Further, if $G$ is second countable, then the Gel'fand space of the commutative convolution algebra $\ccg$ equipped with the inductive limit topology is topologically homeomorphic to $\hg$.
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。
