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Metrizability of totally ordered groups of infinite rank and their completions. (English) Zbl 1131.06012

The authors study topological properties of a canonical family of totally ordered groups, \(\Pi_\alpha,\) and their Dedekind completions \(\Pi_\alpha^{\#}.\) They show that \(\Pi_\alpha^{\#}\) is metrizable if and only if \(\Pi_\alpha\) is countable. In this way they answer a question due to Ochsenius and Schikhof.

MSC:

06F15 Ordered groups
06F30 Ordered topological structures
54E35 Metric spaces, metrizability
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Full Text: Euclid