instUniformSpace — Mathlib

English

The congruence simplification respects the topological space instance; the equality reduces to reflexivity.

Русский

Сходимость данных соответствует топологическому пространству; равенство сводится к рефлексивности.

LaTeX

$$$\\text{UniformConvergenceCLM.instTopologicalSpace congr\_simp}$$$

Lean4

/-- The uniform structure associated with `ContinuousLinearMap.strongTopology`. We make sure
that this has nice definitional properties. -/
instance instUniformSpace [UniformSpace F] [IsUniformAddGroup F] (𝔖 : Set (Set E)) :
    UniformSpace (UniformConvergenceCLM σ F 𝔖) :=
  UniformSpace.replaceTopology ((UniformOnFun.uniformSpace E F 𝔖).comap (UniformOnFun.ofFun 𝔖 ∘ DFunLike.coe))
    (by rw [UniformConvergenceCLM.instTopologicalSpace, IsUniformAddGroup.toUniformSpace_eq]; rfl)

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