Theorems · Theorem · general topology
Metric.dense_iUnion_range_toInductiveLimit
∀ {X : ℕ → Type u} [inst : (n : ℕ) → MetricSpace (X n)] {f : (n : ℕ) → X n → X (n + 1)} (I : ∀ (n : ℕ), Isometry (f n)),
Dense (⋃ i, Set.range (Metric.toInductiveLimit I i))- 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement · cited by 4,705
- Set.univproof · cited by 3,945
- Set.iUnionstatement · cited by 2,483
- MetricSpacestatement and proof · cited by 1,684
- Densestatement · cited by 359
- Isometrystatement and proof · cited by 230
- Set.mem_iUnionproof · cited by 212
- Set.mem_rangeproof · cited by 102
- Dense.monoproof · cited by 43
- dense_univproof · cited by 12
- Metric.InductiveLimitstatement and proof · cited by 4
- Metric.toInductiveLimitstatement · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Metric.separableSpaceInductiveLimit_of_separableSpaceproof · cited by 0