Metrizability of totally ordered groups of infinite rank and their completions
Olivos, E. ; Soto, H. ; Mansilla, A.
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 969-977 / Harvested from Project Euclid
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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 $\Gamma_\alpha^\#$.
Publié le : 2007-12-14
Classification:  Metrizability,  Topological ordered groups,  Topological G-modules,  06F30,  54E35,  06F15,  22B99 
@article{1197908907,
     author = {Olivos, E. and Soto, H. and Mansilla, A.},
     title = {Metrizability of totally ordered groups of infinite rank and their completions},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 969-977},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1197908907}
}

Olivos, E.; Soto, H.; Mansilla, A. Metrizability of totally ordered groups of infinite rank and their completions. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  969-977. http://gdmltest.u-ga.fr/item/1197908907/