Theorems · Definition · global analysis

PartialDiffeomorph.toOpenPartialHomeomorph

{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] →
                        {I : ModelWithCorners 𝕜 E H₁} →
                          {J : ModelWithCorners 𝕜 F H₂} →
                            {M : Type u_8} →
                              [inst_7 : TopologicalSpace M] →
                                [inst_8 : ChartedSpace H₁ M] →
                                  {N : Type u_9} →
                                    [inst_9 : TopologicalSpace N] →
                                      [inst_10 : ChartedSpace H₂ N] →
                                        {n : WithTop ℕ∞} → PartialDiffeomorph I J M N n → OpenPartialHomeomorph M N

A partial diffeomorphism is also a local homeomorphism.

Defined in

Mathlib.Geometry.Manifold.LocalDiffeomorph

Cited by

4 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace