A remark on the Beckman/Quarles theorem

✍ Scribed by Herbert Hotje

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 87 KB
• Volume: 174
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(96)00331-7

✦ Synopsis

BQ) In the distance space (M,d :M ×M -~ A) let k E A and f :M --+M be given such that for all a,b E

Then f is an isometry. The determination of the possible f for a given distance space is called a theorem of Beckman/Quarles type. Here (BQ) is studied for the case of euclidean planes.