Theorems · Inductive type · global analysis

Manifold.IsSmoothEmbedding

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E₁ : Type u_2} →
      {E₃ : Type u_4} →
        [inst_1 : NormedAddCommGroup E₁] →
          [inst_2 : NormedSpace 𝕜 E₁] →
            [inst_3 : NormedAddCommGroup E₃] →
              [inst_4 : NormedSpace 𝕜 E₃] →
                {H : Type u_6} →
                  {G : Type u_8} →
                    [inst_5 : TopologicalSpace H] →
                      [inst_6 : TopologicalSpace G] →
                        ModelWithCorners 𝕜 E₁ H →
                          ModelWithCorners 𝕜 E₃ G →
                            {M : Type u_10} →
                              {N : Type u_12} →
                                [inst : TopologicalSpace M] →
                                  [ChartedSpace H M] →
                                    [inst : TopologicalSpace N] → [ChartedSpace G N] → WithTop ℕ∞ → (M → N) → Prop

A C^n map f : M → M' is a smooth C^n embedding if it is a topological embedding and a C^n immersion.

Defined in

Mathlib.Geometry.Manifold.SmoothEmbedding

Cited by

11 results in Mathlib

Foundations

Depth 12 from the axioms · uses no axioms

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace