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Homeomorphism and Isomorphism of Abelian Groups

Published online by Cambridge University Press:  20 November 2018

Stephen Scheinberg
Stephen Scheinberg*
Affiliation:
University of California, Irvine, Irvine, California
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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 G1andG2are locally compact and connected, then G1≈ G2implies G1= G2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1515 - 1519
Copyright
Copyright © Canadian Mathematical Society 1974

References

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