The Beckman–Quarles theorem via the triangle inequality
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Vilmos Totik
Abstract
We give a short, elementary and non-computational proof for the classical Beckman–Quarles theorem asserting that a map of a Euclidean space into itself that preserves distance 1 must be an isometry.
Communicated by: T. Grundhöfer
References
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Articles in the same Issue
- Frontmatter
- An 𝔽p2-maximal Wiman sextic and its automorphisms
- Pseudo-algebraic Ricci solitons on Einstein nilradicals
- The wobbly divisors of the moduli space of rank-2 vector bundles
- Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
- Betti numbers and pseudoeffective cones in 2-Fano varieties
- The generating rank of a polar Grassmannian
- The Beckman–Quarles theorem via the triangle inequality
- On Huisman’s conjectures about unramified real curves
- Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
- On the Segre invariant for rank two vector bundles on ℙ2
- Lifting coarse homotopies
- How to construct all metric f-K-contact manifolds
- An extremum problem for the power moment of a convex polygon contained in a disc
- Sharply transitive sets in PGL2(K)
Articles in the same Issue
- Frontmatter
- An 𝔽p2-maximal Wiman sextic and its automorphisms
- Pseudo-algebraic Ricci solitons on Einstein nilradicals
- The wobbly divisors of the moduli space of rank-2 vector bundles
- Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
- Betti numbers and pseudoeffective cones in 2-Fano varieties
- The generating rank of a polar Grassmannian
- The Beckman–Quarles theorem via the triangle inequality
- On Huisman’s conjectures about unramified real curves
- Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
- On the Segre invariant for rank two vector bundles on ℙ2
- Lifting coarse homotopies
- How to construct all metric f-K-contact manifolds
- An extremum problem for the power moment of a convex polygon contained in a disc
- Sharply transitive sets in PGL2(K)
