The Beckman-Quarles theorem for mappings from R^2 to F^2, where F is a subfield of a commutative field extending R
| dc.creator | Tyszka, Apoloniusz | |
| dc.date | 2003-07-03 | |
| dc.date | 2005-06-24 | |
| dc.date.accessioned | 2026-07-07T04:59:25Z | |
| dc.date.available | 2026-07-07T04:59:25Z | |
| dc.description | Let F be a subfield of a commutative field extending R. Let ϕ_2: F^2 \times F^2 \to F, ϕ_2((x_1,x_2),(y_1,y_2))=(x_1-y_1)^2+(x_2-y_2)^2. We say that f:R^2 \to F^2 preserves distance d \geq 0 if for each x,y \in R^2 |x-y|=d implies ϕ_2(f(x),f(y))=d^2. We prove that each unit-distance preserving mapping f:R^2 \to F^2 has a form I \circ (ρ,ρ), where ρ: R \to F is a field homomorphism and I: F^2 \to F^2 is an affine mapping with orthogonal linear part. | |
| dc.description | LaTeX2e, 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0307055 | |
| dc.identifier | http://arxiv.org/abs/math/0307055 | |
| dc.identifier | Abh. Math. Sem. Univ. Hamburg 74 (2004), 77-87 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67974 | |
| dc.subject | Metric Geometry | |
| dc.subject | 51M05 | |
| dc.title | The Beckman-Quarles theorem for mappings from R^2 to F^2, where F is a subfield of a commutative field extending R | |
| dc.type | text |