Theorems · Theorem · global analysis

HasStrictFDerivAt.image_mem_toOpenPartialHomeomorph_target

∀ {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} {a : E} [inst_5 : CompleteSpace E] (hf : HasStrictFDerivAt f (↑f') a),
  f a ∈ (HasStrictFDerivAt.toOpenPartialHomeomorph f hf).target

Defined in

Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv

Cited by

3 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace