Beitr\ EMIS ELibM Electronic Journals 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 property

Joseph M. Ling

University of Calgary, Calgary, Alberta, Canada T2N 1N4, e-mail:

Abstract: 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

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Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

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