A uniqueness result for topological groups

Kallman, Robert R.

doi:10.1090/S0002-9939-1976-0417326-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

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A uniqueness result for topological groups
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by Robert R. Kallman

Proc. Amer. Math. Soc. 54 (1976), 439-440

DOI: https://doi.org/10.1090/S0002-9939-1976-0417326-4

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Abstract:

We give a rapid proof of a general result which has an easy corollary that the $p$-adic integers have a unique topology in which they are a complete separable metric group.

References

Lawrence Corwin, Uniqueness of topology for the $p$-adic integers, Proc. Amer. Math. Soc. 55 (1976), no. 2, 432–434. MR 414773, DOI 10.1090/S0002-9939-1976-0414773-1
K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751