Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 185-186 |
| Seitenumfang | 2 |
| Fachzeitschrift | Discrete mathematics |
| Jahrgang | 174 |
| Ausgabenummer | 1-3 |
| Publikationsstatus | Veröffentlicht - 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 Sachgebiete
- Mathematik (insg.)
- Theoretische Informatik
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
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in: Discrete mathematics, Jahrgang 174, Nr. 1-3, 15.09.1997, S. 185-186.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -