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A characterization of isometries on an open convex set, II
- Authors
- Jung, Soon-Mo
- Issue Date
- Mar-2009
- Publisher
- SPRINGER
- Keywords
- Aleksandrov problem; isometry; distance preserving mapping; restricted domain
- Citation
- BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v.40, no.1, pp.77 - 84
- Journal Title
- BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
- Volume
- 40
- Number
- 1
- Start Page
- 77
- End Page
- 84
- ISSN
- 1678-7544
- 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 C(0) of En into E(n), preserves a distance rho, then the restriction of f to an open convex subset C(infinity) of C(0) is an isometry.
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