Some theorems on the metrization of Abelian groups

The results of this paper are concerned with the construction of a metrizable topology $\nu$ on an infinite Abelian group $G$, compatible with the group structure, such that the completion $\nu G$ of the group $(G,\nu)$ is arcwise connected and locally arcwise connected.
As an application of these results, we describe a method by which any metrizable Abelian group of weight $\mathbf m$ can be imbedded as a closed subgroup of an arcwise connected and locally arcwise connected metrizable Abelian group of weight $\max(\mathbf m,\aleph_0)$.
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