Geodesic
Some theorems on the metrization of Abelian groups
Sbornik. Mathematics, Tome 23 (1974) no. 3, pp. 319-335

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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 $\max(\mathbf m,\aleph_0)$. Bibliography: 12 titles. 
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     author = {V. K. Bel'nov},
     title = {Some theorems on the metrization of {Abelian} groups},
     journal = {Sbornik. Mathematics},
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     number = {3},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_23_3_a0/}
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V. K. Bel'nov. Some theorems on the metrization of Abelian groups. Sbornik. Mathematics, Tome 23 (1974) no. 3, pp. 319-335. http://geodesic.mathdoc.fr/item/SM_1974_23_3_a0/