Theorems · Theorem · real analysis

ContDiffWithinAt.comp_continuousLinearMap

∀ {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} {n : WithTop ℕ∞} {x : G}
  (g : G →L[𝕜] E), ContDiffWithinAt 𝕜 n f s (g x) → ContDiffWithinAt 𝕜 n (f ∘ ⇑g) (⇑g ⁻¹' s) x

Composition by continuous linear maps on the right preserves C^n functions at a point on a domain.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Basic

Cited by

2 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace