Details
| Original language | English |
|---|---|
| Pages (from-to) | 185-186 |
| Number of pages | 2 |
| Journal | Discrete mathematics |
| Volume | 174 |
| Issue number | 1-3 |
| Publication status | Published - 15 Sept 1997 |
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.
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Discrete mathematics, Vol. 174, No. 1-3, 15.09.1997, p. 185-186.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A remark on the Beckman/Quarles theorem
AU - Hotje, Herbert
PY - 1997/9/15
Y1 - 1997/9/15
N2 - (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.
AB - (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.
UR - http://www.scopus.com/inward/record.url?scp=30244476448&partnerID=8YFLogxK
U2 - 10.1016/S0012-365X(96)00331-7
DO - 10.1016/S0012-365X(96)00331-7
M3 - Article
AN - SCOPUS:30244476448
VL - 174
SP - 185
EP - 186
JO - Discrete mathematics
JF - Discrete mathematics
SN - 0012-365X
IS - 1-3
ER -