On mappings of ℚd to ℚd that preserve distances 1 and √2 and the Beckman-Quarles Theorem

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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 languageEnglish
Pages (from-to)195-203
Number of pages9
JournalJournal of Geometry
Volume82
Issue number1-2
DOIs
StatePublished - Aug 2005

Keywords

  • Beckman-Quarles Theorem
  • Distance preserving mappings
  • Isometry

ASJC Scopus subject areas

  • Geometry and Topology

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