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, ??, and their completions ?? #. Furthermore we obtain for this family conditions both necessary and sufficient for the metrizability of ?? #.