## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Metrizability of totally ordered groups of infinite rank and their completions

#### Abstract

In [4], Ochsenius and Schikhof ask the following question. Given a totally ordered group $G$ with a cofinal sequence, if every element of its Dedekind completion $G^\#$ is the supremum of a sequence in $G$, does it follow that $G^\#$ is metrizable? We answer their question by studying topological properties of a family of totally ordered groups, $\Gamma_\alpha$, and their completions $\Gamma_\alpha^\#$. Furthermore we obtain for this family conditions both necessary and sufficient for the metrizability of $\Gamma_\alpha^\#$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 5 (2007), 969-977.

Dates
First available in Project Euclid: 17 December 2007

https://projecteuclid.org/euclid.bbms/1197908907

Digital Object Identifier
doi:10.36045/bbms/1197908907

Mathematical Reviews number (MathSciNet)
MR2379001

Zentralblatt MATH identifier
1131.06012

#### Citation

Olivos, E.; Soto, H.; Mansilla, A. Metrizability of totally ordered groups of infinite rank and their completions. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 5, 969--977. doi:10.36045/bbms/1197908907. https://projecteuclid.org/euclid.bbms/1197908907