A Locally Compact Non Divisible Abelian Group Whose Character Group Is Torsion Free and Divisible

Canadian mathematical bulletin

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