Theorems · Definition · global analysis

IsLocalDiffeomorphAt

{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] →
                {H₁ : Type u_5} →
                  [inst_5 : TopologicalSpace H₁] →
                    {H₂ : Type u_6} →
                      [inst_6 : TopologicalSpace H₂] →
                        ModelWithCorners 𝕜 E H₁ →
                          ModelWithCorners 𝕜 F H₂ →
                            {M : Type u_8} →
                              [inst : TopologicalSpace M] →
                                [ChartedSpace H₁ M] →
                                  {N : Type u_9} →
                                    [inst : TopologicalSpace N] → [ChartedSpace H₂ N] → WithTop ℕ∞ → (M → N) → M → Prop

f : M → N is called a `C^n` local diffeomorphism at `x` iff there exist open sets U ∋ x and V ∋ f x and a diffeomorphism Φ : U → V such that f = Φ on U.

Defined in

Mathlib.Geometry.Manifold.LocalDiffeomorph

Cited by

23 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace