Uniqueness of topology for the $p$-adic integers
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- by Lawrence Corwin
- Proc. Amer. Math. Soc. 55 (1976), 432-434
- DOI: https://doi.org/10.1090/S0002-9939-1976-0414773-1
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Abstract:
It is shown that the only Hausdorff topologies on ${{\mathbf {Z}}_p}$, the $p$-adic integers, which make it into a locally compact Abelian group are the $p$-adic and discrete topologies. The key ingredient in the proof is a structure theorem for certain LCA groups which may be of independent interest.References
- Lawrence Corwin, Generalized Gaussian measure and a “functional equation”. I, J. Functional Analysis 5 (1970), 412–427. MR 0259497, DOI 10.1016/0022-1236(70)90018-2
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496, DOI 10.1007/978-1-4419-8638-2
- Robert R. Kallman, The topology of compact simple Lie groups is essentially unique, Advances in Math. 12 (1974), 416–417. MR 357677, DOI 10.1016/S0001-8708(74)80010-1
- Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
- George W. Mackey, A remark on locally compact Abelian groups, Bull. Amer. Math. Soc. 52 (1946), 940–944. MR 18648, DOI 10.1090/S0002-9904-1946-08685-1
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 432-434
- MSC: Primary 22B05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0414773-1
- MathSciNet review: 0414773