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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A group-theoretic property of the Euclidean metric


Authors: Robert Williamson and Ludvik Janos
Journal: Proc. Amer. Math. Soc. 98 (1986), 150-152
MSC: Primary 54E35; Secondary 54E40, 54H15
MathSciNet review: 848893
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0848893-0
PII: S 0002-9939(1986)0848893-0
Article copyright: © Copyright 1986 American Mathematical Society