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A characterization of isometries on an open convex set, II

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Abstract

Let E n be an n-dimensional Euclidean space with n ≥ 2. In this paper, we generalize a classical theorem of Beckman and Quarles by proving that if a mapping, from an open convex subset Co of E n into E n, preserves a distance ρ, then the restriction of f to an open convex subset C ∞ of C 0 is an isometry.

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Authors and Affiliations

  1. Mathematics Section College of Science and Technology, Hong-Ik University, 339-701, Chochiwon, Korea

    Soon-Mo Jung

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  1. Soon-Mo Jung
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Correspondence to Soon-Mo Jung.

Additional information

This work was supported by 2007 Hongik University Research Fund.

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Jung, SM. A characterization of isometries on an open convex set, II. Bull Braz Math Soc, New Series 40, 77–84 (2009). https://doi.org/10.1007/s00574-009-0003-2

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  • DOI: https://doi.org/10.1007/s00574-009-0003-2

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