Theorems · Definition · general topology
IsometryEquiv.toDilationEquiv
{X : Type u_1} → {Y : Type u_2} → [inst : PseudoEMetricSpace X] → [inst_1 : PseudoEMetricSpace Y] → X ≃ᵢ Y → X ≃ᵈ YEvery isometry equivalence is a dilation equivalence of ratio 1.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 158 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.
- Equivproof · cited by 8,337
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsometryEquivstatement and proof · cited by 177
- DilationEquivstatement · cited by 55
- IsometryEquiv.toEquivproof · cited by 33
Cited by6
Results whose statement or proof uses this declaration.
- IsometryEquiv.toDilationEquiv_toDilationstatement · cited by 1
- IsometryEquiv.coe_symm_toDilationEquivstatement · cited by 0
- IsometryEquiv.toDilationEquiv_applystatement · cited by 0
- IsometryEquiv.toDilationEquiv_ratiostatement and proof · cited by 0
- IsometryEquiv.toDilationEquiv_symmstatement · cited by 0
- IsometryEquiv.coe_toDilationEquivstatement · cited by 0