Theorems · Theorem · general topology
Isometry.edist_eq
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
Isometry f → ∀ (x y : α), edist (f x) (f y) = edist x yAn isometry preserves edistances.
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement · cited by 735
- Isometrystatement and proof · cited by 230
Cited by18
Results whose statement or proof uses this declaration.
- Isometry.ediam_imageproof · cited by 12
- Metric.infEDist_imageproof · cited by 7
- Isometry.preimage_closedEBallproof · cited by 3
- Isometry.preimage_eballproof · cited by 3
- Isometry.isCover_image_iffproof · cited by 1
- Isometry.lipschitzWith_iffproof · cited by 1
- IsometryEquiv.edist_eqproof · cited by 1
- lipschitzOnWith_cfc_funproof · cited by 1
- lipschitzOnWith_cfcₙ_funproof · cited by 1
- LinearIsometry.edist_mapproof · cited by 1
- Isometry.prodMapproof · cited by 1
- enorm_sub_le_lintegral_deriv_of_contDiffOn_Iccproof · cited by 1