InductiveLimit — Mathlib

English

The inductive limit is the SeparationQuotient of the inductivePremetric's underlying uniform/topological space.

Русский

Индуктивный предел является SeparationQuotient от соответствующего унитарного/топологического пространства inductivePremetric.

LaTeX

$$$\text{InductiveLimit}(I) = \mathrm{SeparationQuotient}\left(\operatorname{inductivePremetric}(I)\right)$$$

Lean4

/-- The type giving the inductive limit in a metric space context. -/
def InductiveLimit (I : ∀ n, Isometry (f n)) : Type _ :=
  @SeparationQuotient _ (inductivePremetric I).toUniformSpace.toTopologicalSpace

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