Theorems · Theorem · general topology
IsometryEquiv.completeSpace_iff
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (e : α ≃ᵢ β),
CompleteSpace α ↔ CompleteSpace β- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.univproof · cited by 3,945
- CompleteSpacestatement · cited by 2,532
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsometryEquivstatement and proof · cited by 177
- IsCompleteproof · cited by 68
- IsometryEquiv.isometryproof · cited by 22
- Isometry.isUniformInducingproof · cited by 10
- isComplete_image_iffproof · cited by 5
- IsometryEquiv.range_eq_univproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- IsometryEquiv.completeSpaceproof · cited by 0