Theorems · Definition · global analysis

ContDiffAt.toOpenPartialHomeomorph

{𝕂 : Type u_1} →
  [inst : RCLike 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] →
                [CompleteSpace E] →
                  (f : E → F) →
                    {f' : E ≃L[𝕂] F} →
                      {a : E} →
                        {n : WithTop ℕ∞} →
                          ContDiffAt 𝕂 n f a → HasFDerivAt f (↑f') a → n ≠ 0 → OpenPartialHomeomorph E F

Given a ContDiff function over 𝕂 (which is ℝ or ℂ) with an invertible derivative at a, returns an OpenPartialHomeomorph with to_fun = f and a ∈ source.

Defined in

Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff

Cited by

4 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace