Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T13:18:58.667Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Eilenberg, S. and Steenrod, N., Foundations of algebraic topology (Princeton Univ. Press Princeton, 1952).Google Scholar
2. Hocking, J. G. and Young, G. S., Topology (Addison-Wesley, Reading, Mass., 1961).Google Scholar
3. Kaplansky, I., Infinite abelian groups (U. of Michigan Press, Ann Arbor, 1954).Google Scholar
4. Mazur, S., Une remarque sur l'homéomorphie des champs fonctionnels, Studia Math. 1 (1929), 83–85.Google Scholar
5. Rudin, W., Fourier analysis on groups (Wiley (Interscience), New York, 1962).Google Scholar
6. Scheinberg, S., Homeomorphic isomorphic abelian groups, Notices Amer. Math. Soc. II (1964), 464.Google Scholar