Theorems · Definition · algebraic topology

VectorPrebundle.contMDiffCoordChange

(n : WithTop ℕ∞) →
  {𝕜 : Type u_1} →
    {B : Type u_2} →
      {F : Type u_4} →
        {E : B → Type u_6} →
          [inst : NontriviallyNormedField 𝕜] →
            {EB : Type u_7} →
              [inst_1 : NormedAddCommGroup EB] →
                [inst_2 : NormedSpace 𝕜 EB] →
                  {HB : Type u_8} →
                    [inst_3 : TopologicalSpace HB] →
                      (IB : ModelWithCorners 𝕜 EB HB) →
                        [inst_4 : TopologicalSpace B] →
                          [inst_5 : ChartedSpace HB B] →
                            [inst_6 : (x : B) → AddCommMonoid (E x)] →
                              [inst_7 : (x : B) → Module 𝕜 (E x)] →
                                [inst_8 : NormedAddCommGroup F] →
                                  [inst_9 : NormedSpace 𝕜 F] →
                                    [inst_10 : (x : B) → TopologicalSpace (E x)] →
                                      (a : VectorPrebundle 𝕜 F E) →
                                        [ha : VectorPrebundle.IsContMDiff IB a n] →
                                          {e e' : Bundle.Pretrivialization F Bundle.TotalSpace.proj} →
                                            e ∈ a.pretrivializationAtlas → e' ∈ a.pretrivializationAtlas → B → F →L[𝕜] F

A randomly chosen coordinate change on a VectorPrebundle satisfying IsContMDiff, given by the field exists_coordChange. Note that a.contMDiffCoordChange need not be the same as a.coordChange.

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Basic

Cited by

3 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceVectorPrebundle.IsContMDiff