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Theorems · Definition · general topology

Metric.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)) → (n : ℕ) → X n → Metric.InductiveLimit I

Mapping each X n to the inductive limit.

Defined in
Mathlib.Topology.MetricSpace.Gluing
Cited by
4 results in Mathlib
Foundations
Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MetricSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Metric.toInductiveLimit_isometry · cited by 1Metric.toInductiveLimit_i…Metric.dense_iUnion_range_toInductiveLimit · cited by 1Metric.dense_iUnion_range…Metric.separableSpaceInductiveLimit_of_separableSpace · cited by 0Metric.separableSpaceIndu…Metric.toInductiveLimit_commute · cited by 0Metric.toInductiveLimit_c…MetricSpace · cited by 1684MetricSpaceIsometry · cited by 230IsometryQuotient.mk'' · cited by 132Quotient.mk''Metric.InductiveLimit · cited by 4Metric.InductiveLimitMetric.toInductiveLimitCITED BYCITES

Cites4

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Cited by4

Results whose statement or proof uses this declaration.