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

作者：Tausk Daniel V^*

来源：Canadian Mathematical Bulletin, 2013, 56(1): 213-217.

DOI：10.4153/CMB-2011-146-4

It was claimed by Halmos in 1944 that if G is a Hausdorff locally compact topological abelian group and if the character group of G is torsion free, then G is divisible. We prove that such a claim is false by presenting 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.

• 出版日期2013-3