A discrete form of the Beckman-Quarles theorem for two-dimensional strictly convex normed spaces
| dc.creator | Tyszka, Apoloniusz | |
| dc.date | 2000-08-17 | |
| dc.date | 2000-10-08 | |
| dc.date.accessioned | 2026-07-07T04:36:52Z | |
| dc.date.available | 2026-07-07T04:36:52Z | |
| dc.description | Let X be a real normed vector space and dim X \ge 2. Let d>0 be a fixed real number. We prove that if x,y \in X and ||x-y||/d is a rational number then there exists a finite set {x,y} \subseteq S(x,y) \subseteq X with the following property: for each strictly convex Y of dimension 2 each map from S(x,y) to Y preserving the distance d preserves the distance between x and y. It implies that each map from X to Y that preserves the distance d is an isometry. | |
| dc.description | LaTeX 2.09, with a note that S(x,y) does not depend on Y | |
| dc.identifier | https://arxiv.org/abs/math/0008135 | |
| dc.identifier | http://arxiv.org/abs/math/0008135 | |
| dc.identifier | Nonlinear Functional Analysis and Applications 7 (2002), pp.353-360 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59755 | |
| dc.subject | Functional Analysis | |
| dc.subject | Metric Geometry | |
| dc.subject | 46B20 | |
| dc.title | A discrete form of the Beckman-Quarles theorem for two-dimensional strictly convex normed spaces | |
| dc.type | text |