Theorems · Definition · global analysis

Manifold.SubmersionAtProp

{𝕜 : Type u_1} →
  {E'' : Type u_3} →
    (F : Type u_5) →
      {H : Type u_7} →
        {G : Type u_9} →
          {E : Type u} →
            [inst : NontriviallyNormedField 𝕜] →
              [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] →
                          [inst_7 : TopologicalSpace H] →
                            [inst_8 : TopologicalSpace G] →
                              ModelWithCorners 𝕜 E H →
                                ModelWithCorners 𝕜 E'' G →
                                  (M : Type u_11) →
                                    (N : Type u_13) →
                                      [inst : TopologicalSpace M] →
                                        [inst_9 : TopologicalSpace N] →
                                          (M → N) → OpenPartialHomeomorph M H → OpenPartialHomeomorph N G → Prop

The local property of being a submersion at a point: f : M → N is a submersion 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 projection (u, v) ↦ u. This definition has a fixed parameter F, which is a choice of complement of E'' in the model normed space E of M: being a submersion at x includes a choice of linear isomorphism between E'' × F and E.

Defined in

Mathlib.Geometry.Manifold.Submersion

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace