Theorems · Theorem · general topology
Metric.toInductiveLimit_isometry
∀ {X : ℕ → Type u} [inst : (n : ℕ) → MetricSpace (X n)] {f : (n : ℕ) → X n → X (n + 1)} (I : ∀ (n : ℕ), Isometry (f n))
(n : ℕ), Isometry (Metric.toInductiveLimit I n)The map toInductiveLimit n mapping X n to the inductive limit is an isometry.
- Defined in
- Mathlib.Topology.MetricSpace.Gluing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- le_reflproof · cited by 2,061
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- Isometrystatement and proof · cited by 230
- Isometry.of_dist_eqproof · cited by 27
- Nat.leRecOnproof · cited by 13
- Nat.leRecOn_selfproof · cited by 5
- Metric.InductiveLimitstatement · cited by 4
- Metric.toInductiveLimitstatement · cited by 4
- Metric.inductiveLimitDist_eq_distproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Metric.separableSpaceInductiveLimit_of_separableSpaceproof · cited by 0