Theorems · Theorem · general topology
IsometryEquiv.range_eq_univ
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (h : α ≃ᵢ β),
Set.range ⇑h = Set.univ- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Set.rangestatement · cited by 4,705
- Set.univstatement and proof · cited by 3,945
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsometryEquivstatement and proof · cited by 177
- EquivLike.range_eq_univproof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- GromovHausdorff.eq_toGHSpace_iffproof · cited by 3
- IsometryEquiv.ediam_univproof · cited by 1
- IsometryEquiv.completeSpace_iffproof · cited by 1
- AffineIsometryEquiv.range_eq_univproof · cited by 0
- LinearIsometryEquiv.range_eq_univproof · cited by 0