期刊论文详细信息
Canadian mathematical bulletin | |
A Locally Compact Non Divisible Abelian Group Whose Character Group Is Torsion Free and Divisible | |
Daniel V. Tausk1  | |
[1] Departamento de Matemática, Universidade de São Paulo, Brazil | |
关键词: productively Lindelöf; $D$-space; projectively $sigma$-compact; Menger; Hurewicz; | |
DOI : 10.4153/CMB-2011-146-4 | |
学科分类:数学(综合) | |
来源: University of Toronto Press * Journals Division | |
【 摘 要 】
It was claimed by Halmos in 1944 that if $G$ is a Hausdorff locally compact topological abeliangroup and if the character group of $G$ is torsion free, then $G$ is divisible. We prove that such a claim is false bypresenting a family of counterexamples. While other counterexamples are known, we also present a family of stronger counterexamples,showing that even if one assumes that the character group of $G$ is both torsion free and divisible, it does not follow that $G$ is divisible.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201912050576934ZK.pdf | 35KB | download |