Theorems · Definition · general topology
Fin.appendIsometry
{α : Type u} → [inst : PseudoEMetricSpace α] → (m n : ℕ) → (Fin m → α) × (Fin n → α) ≃ᵢ (Fin (m + n) → α)The natural IsometryEquiv between (Fin m → α) × (Fin n → α) and Fin (m + n) → α.
Fin.appendEquiv as an IsometryEquiv.
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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.
- Equivproof · cited by 8,337
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsometryEquivstatement · cited by 177
- Fin.appendEquivproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Fin.appendIsometryOfEqproof · cited by 2
- Fin.appendIsometry_applystatement and proof · cited by 0
- Fin.appendIsometry_symm_applystatement and proof · cited by 0
- Fin.appendIsometry_toHomeomorphstatement · cited by 0