Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 48, No. 1, pp. 131-139 (2007)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 1, pp. 131-139 (2007) |
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A normed space with the Beckman-Quarles propertyJoseph M. LingUniversity of Calgary, Calgary, Alberta, Canada T2N 1N4, e-mail: ling@math.ucalgary.caAbstract: Beckman and Quarles proved that a unit distance preserving mapping from a Euclidean space $\mathbf{E}^{n}$ into itself is necessarily an isometry. In this paper, we give an example of a (non-strictly convex) normed space $H$ for which every unit distance preserving function from $H$ into itself is an isometry. Keywords: Beckman-Quarles theorem, isometry Classification (MSC2000): 51M05, 52A10, 52A20, 52C05, 52C25 Full text of the article:
Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.
© 2007 Heldermann Verlag
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