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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Uniqueness of topology for the $ p$-adic integers


Author: Lawrence Corwin
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0414773-1
Keywords: Locally compact Abelian group, $ p$-adic integers, uniquely divisible by a prime
Article copyright: © Copyright 1976 American Mathematical Society