Theorems · Theorem · global analysis

ApproximatesLinearOn.injective

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {f' : E ≃L[𝕜] F} {s : Set E} {c : NNReal},
  ApproximatesLinearOn f (↑f') s c → Subsingleton E ∨ c < ‖↑f'.symm‖₊⁻¹ → Function.Injective (s.domRestrict f)

Defined in

Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn

Cited by

1 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace