Theorems · Theorem · general topology
Isometry.diam_range
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {f : α → β},
Isometry f → Metric.diam (Set.range f) = Metric.diam Set.univ- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement · cited by 25,697
- Set.rangestatement · cited by 4,705
- Set.univstatement and proof · cited by 3,945
- PseudoMetricSpacestatement and proof · cited by 1,550
- Set.image_univproof · cited by 322
- Isometrystatement and proof · cited by 230
- Metric.diamstatement and proof · cited by 74
- Isometry.diam_imageproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- GromovHausdorff.hausdorffDist_optimalproof · cited by 1
- AffineIsometry.diam_rangeproof · cited by 0
- LinearIsometry.diam_rangeproof · cited by 0
- SemilinearIsometryClass.diam_rangeproof · cited by 0
- IsometryClass.diam_rangeproof · cited by 0