Geodesic
Homeomorphism and Isomorphism of Abelian Groups
Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1515-1519

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An abelian topological group can be considered simply as an abelian group or as a topological space. The question considered in this article is whether the topological group structure is determined by these weaker structures. Denote homeomorphism, isomorphism, and homeomorphic isomorphism by ≈, ≅ , and =, respectively. The principal results are these.Theorem 1. If G 1andG 2are locally compact and connected, then G 1≈ G 2implies G 1= G 2. 
Scheinberg, Stephen. Homeomorphism and Isomorphism of Abelian Groups. Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1515-1519. doi: 10.4153/CJM-1974-147-4
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