The Beckman-Quarles theorem for mappings from \(\mathbb{R}^2\) of \(\mathbb{F}^2\), where \(\mathbb{F}\) is a subfield of a commutative field extending \(\mathbb{R}\)
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Publication:1766169
DOI10.1007/BF02941526zbMath1067.51010arXivmath/0307055OpenAlexW2064565443MaRDI QIDQ1766169
Publication date: 28 February 2005
Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0307055
Beckman-Quarles theoremCayley-Menger determinant(semi-)affine isometry(semi-)affine mapping with orthogonal linear partdistance-preserving mapping
Cites Work
- A discrete form of the Beckman-Quarles theorem for mappings from \(\mathbb{R}^2\,(\mathbb{C}^2)\) to \(\mathbb{F}^2\), where \(\mathbb{F}\) is a subfield of a commutative field extending \(\mathbb{R}\,(\mathbb{C})\)
- An elementary proof of the theorem of Beckman and Quarles
- Beckman-Quarles type theorems for mappings from \(\mathbb{R}^n\) to \(\mathbb{C}^n\)
- On Isometries of Euclidean Spaces
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