Theorems · Definition · global analysis

Manifold.ImmersionAtProp

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      {E'' : Type u} →
        (F : Type u_5) →
          [inst_1 : NormedAddCommGroup E] →
            [inst_2 : NormedSpace 𝕜 E] →
              [inst_3 : NormedAddCommGroup E''] →
                [inst_4 : NormedSpace 𝕜 E''] →
                  [inst_5 : NormedAddCommGroup F] →
                    [NormedSpace 𝕜 F] →
                      {H : Type u_7} →
                        [inst_7 : TopologicalSpace H] →
                          {G : Type u_9} →
                            [inst_8 : TopologicalSpace G] →
                              ModelWithCorners 𝕜 E H →
                                ModelWithCorners 𝕜 E'' G →
                                  (M : Type u_11) →
                                    [inst : TopologicalSpace M] →
                                      (N : Type u_13) →
                                        [inst_9 : TopologicalSpace N] →
                                          (M → N) → OpenPartialHomeomorph M H → OpenPartialHomeomorph N G → Prop

The local property of being an immersion at a point: f : M → N is an immersion at x if there exist charts φ and ψ of M and N around x and f x, respectively, such that in these charts, f looks like the inclusion u ↦ (u, 0). This definition has a fixed parameter F, which is a choice of complement of E in the model normed space E' of N: being an immersion at x includes a choice of linear isomorphism between E × F and E'.

Defined in

Mathlib.Geometry.Manifold.Immersion

Cited by

4 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace