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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)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A group-theoretic property of the Euclidean metric
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by Robert Williamson and Ludvik Janos PDF
Proc. Amer. Math. Soc. 98 (1986), 150-152 Request permission

Abstract:

Let $d$ denote a metric on ${{\mathbf {R}}^n}(n \in {\mathbf {N}})$ compatible with its Euclidean toplogy, and let $I(d)$ be the group of isometries on ${{\mathbf {R}}^n}$ relative to this metric. We show that whenever $I(d)$ includes the group of motions then $I(d)$ is identical with it.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 98 (1986), 150-152
  • MSC: Primary 54E35; Secondary 54E40, 54H15
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0848893-0
  • MathSciNet review: 848893