Theorems · Theorem · general topology
Isometry.dist_eq
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {f : α → β},
Isometry f → ∀ (x y : α), dist (f x) (f y) = dist x yAn isometry preserves distances.
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 21 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 by21
Results whose statement or proof uses this declaration.
- Isometry.norm_map_of_map_zeroproof · cited by 13
- IsometryEquiv.dist_eqproof · cited by 6
- Isometry.preimage_setOfPred_distproof · cited by 4
- Isometry.completion_extensionproof · cited by 4
- dist_vaddproof · cited by 4
- ODE.FunSpace.dist_iterate_next_iterate_next_leproof · cited by 2
- Isometry.norm_map_of_map_oneproof · cited by 2
- dist_smulproof · cited by 2
- LinearIsometry.dist_mapproof · cited by 2
- Complex.isometry_intCastproof · cited by 2
- Isometry.cosphericalproof · cited by 2
- GromovHausdorff.hausdorffDist_optimalproof · cited by 1