Theorems · Definition · global analysis

equivTangentBundleProd

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

The tangent bundle of a product is canonically isomorphic to the product of the tangent bundles.

Defined in

Mathlib.Geometry.Manifold.ContMDiffMFDeriv

Cited by

8 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace