Theorems · Theorem · real analysis

ContinuousLinearEquiv.contDiffWithinAt_comp_iff

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {s : Set E} {f : E → F} {x : E} {n : WithTop ℕ∞}
  (e : G ≃L[𝕜] E), ContDiffWithinAt 𝕜 n (f ∘ ⇑e) (⇑e ⁻¹' s) (e.symm x) ↔ ContDiffWithinAt 𝕜 n f s x

Composition by continuous linear equivs on the right respects higher differentiability at a point in a domain.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Basic

Cited by

1 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace