A remark on the Beckman/Quarles theorem

authored by

Herbert Hotje

Abstract

(BQ) In the distance space (M, d : M × M → Δ) let k ∈ Δ and f : M → M be given such that for all a,b ∈ M: d(a,b) = k ⇒ d(f(a),f(b)) = k. 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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Discrete mathematics

Volume

174

Pages

185-186

No. of pages

2

ISSN

0012-365X

Publication date

15.09.1997

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Theoretical Computer Science, Discrete Mathematics and Combinatorics

Electronic version(s)

https://doi.org/10.1016/S0012-365X(96)00331-7 (Access: Open)