Theorems · Definition · global analysis

VectorField.mpullbackWithin

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {H : Type u_2} →
      [inst_1 : TopologicalSpace H] →
        {E : Type u_3} →
          [inst_2 : NormedAddCommGroup E] →
            [inst_3 : NormedSpace 𝕜 E] →
              (I : ModelWithCorners 𝕜 E H) →
                {M : Type u_4} →
                  [inst_4 : TopologicalSpace M] →
                    [inst_5 : ChartedSpace H M] →
                      {H' : Type u_5} →
                        [inst_6 : TopologicalSpace H'] →
                          {E' : Type u_6} →
                            [inst_7 : NormedAddCommGroup E'] →
                              [inst_8 : NormedSpace 𝕜 E'] →
                                (I' : ModelWithCorners 𝕜 E' H') →
                                  {M' : Type u_7} →
                                    [inst_9 : TopologicalSpace M'] →
                                      [inst_10 : ChartedSpace H' M'] →
                                        (M → M') → ((x : M') → TangentSpace I' x) → Set M → (x : M) → TangentSpace I x

The pullback of a vector field under a map between manifolds, within a set s. If the derivative of the map within s is not invertible, then pullback is given the junk value zero.

Defined in

Mathlib.Geometry.Manifold.VectorField.Pullback

Cited by

48 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpace