Open Access
December 2007 Metrizability of totally ordered groups of infinite rank and their completions
A. Mansilla, E. Olivos, H. Soto
Bull. Belg. Math. Soc. Simon Stevin 14(5): 969-977 (December 2007). DOI: 10.36045/bbms/1197908907


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 $\Gamma_\alpha^\#$.


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A. Mansilla. E. Olivos. H. Soto. "Metrizability of totally ordered groups of infinite rank and their completions." Bull. Belg. Math. Soc. Simon Stevin 14 (5) 969 - 977, December 2007.


Published: December 2007
First available in Project Euclid: 17 December 2007

zbMATH: 1131.06012
MathSciNet: MR2379001
Digital Object Identifier: 10.36045/bbms/1197908907

Primary: 06F30 , 54E35
Secondary: 06F15 , 22B99

Keywords: Metrizability , Topological G-modules , Topological ordered groups

Rights: Copyright © 2007 The Belgian Mathematical Society

Vol.14 • No. 5 • December 2007
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