Abstract
Benz proved that every mapping f : ℚd → ℚd that preserves the distances 1 and 2 is an isometry, provided d ≥ 5. We prove that every mapping f : ℚd → ℚd that preserves the distances 1 and √2 is an isometry, provided d ≥ 5.
Original language | English |
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Pages (from-to) | 195-203 |
Number of pages | 9 |
Journal | Journal of Geometry |
Volume | 82 |
Issue number | 1-2 |
DOIs | |
State | Published - Aug 2005 |
Keywords
- Beckman-Quarles Theorem
- Distance preserving mappings
- Isometry
ASJC Scopus subject areas
- Geometry and Topology