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Uniqueness of Topology for the $p$-Adic Integers

Lawrence Corwin
Proceedings of the American Mathematical Society
Vol. 55, No. 2 (Mar., 1976), pp. 432-434
DOI: 10.2307/2041740
Stable URL: http://www.jstor.org/stable/2041740
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Uniqueness of Topology for the $p$-Adic Integers
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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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