A locally compact non divisible abelian group whose character group is torsion free and divisible

Details A locally compact non divisible abelian group whose character group is torsion free and divisible A locally compact non divisible abelian group whose character group is torsion free and divisible

2010-02-22

arxiv.org/abs/1002.4164v2

Mathematics

General Topology

5 pages, 0 figures

Scientific paper

It has been claimed by Halmos in [Comment on the real line, Bull. Amer. Math. Soc., 50 (1944), 877-878] 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 claim is false, by presenting a family of counterexamples. While other counterexamples are known (see [D. L. Armacost, The structure of locally compact abelian groups, 1981]), 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.

Affiliated with

Also associated with

No associations

Rating

A locally compact non divisible abelian group whose character group is torsion free and divisible does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A locally compact non divisible abelian group whose character group is torsion free and divisible, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A locally compact non divisible abelian group whose character group is torsion free and divisible will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-374002