Theorems · Definition · general topology
Metric.InductiveLimit
{X : ℕ → Type u} →
[inst : (n : ℕ) → MetricSpace (X n)] → {f : (n : ℕ) → X n → X (n + 1)} → (∀ (n : ℕ), Isometry (f n)) → Type uThe type giving the inductive limit in a metric space context.
- Defined in
- Mathlib.Topology.MetricSpace.Gluing
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 157 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MetricSpacestatement and proof · cited by 1,684
- Isometrystatement and proof · cited by 230
- SeparationQuotientproof · cited by 128
Cited by5
Results whose statement or proof uses this declaration.
- Metric.toInductiveLimitstatement · cited by 4
- Metric.toInductiveLimit_isometrystatement · cited by 1
- Metric.dense_iUnion_range_toInductiveLimitstatement and proof · cited by 1
- Metric.toInductiveLimit_commutestatement · cited by 0
- Metric.separableSpaceInductiveLimit_of_separableSpacestatement and proof · cited by 0