Theorems · Theorem · general topology
Isometry.of_dist_eq
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {f : α → β},
(∀ (x y : α), dist (f x) (f y) = dist x y) → Isometry fA map that preserves distances is an isometry
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Isometrystatement · cited by 230
- isometry_iff_dist_eqproof · cited by 3
Cited by27
Results whose statement or proof uses this declaration.
- Isometry.completion_extensionproof · cited by 4
- algebraMap_isometryproof · cited by 4
- Topology.IsEmbedding.to_isometryproof · cited by 3
- UniformSpace.Completion.coe_isometryproof · cited by 3
- NumberField.InfinitePlace.Completion.isometry_toCompletionproof · cited by 3
- GromovHausdorff.isometry_optimalGHInjlproof · cited by 2
- GromovHausdorff.isometry_optimalGHInjrproof · cited by 2
- Complex.isometry_intCastproof · cited by 2
- GromovHausdorff.ghDist_le_of_approx_subsetsproof · cited by 1
- KuratowskiEmbedding.embeddingOfSubset_isometryproof · cited by 1
- Real.isometry_intCastproof · cited by 1
- Metric.toInductiveLimit_isometryproof · cited by 1