Theorems · Theorem · algebraic topology

contMDiffOn_symm_coordChangeL

∀ {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 : TopologicalSpace (Bundle.TotalSpace F E)]
  [inst_11 : (x : B) → TopologicalSpace (E x)] [inst_12 : FiberBundle F E] [inst_13 : VectorBundle 𝕜 F E]
  [ContMDiffVectorBundle n F E IB] (e e' : Bundle.Trivialization F Bundle.TotalSpace.proj)
  [inst_15 : MemTrivializationAtlas e] [inst_16 : MemTrivializationAtlas e'],
  ContMDiffOn IB (modelWithCornersSelf 𝕜 (F →L[𝕜] F)) n (fun b => ↑(Bundle.Trivialization.coordChangeL 𝕜 e e' b).symm)
    (e.baseSet ∩ e'.baseSet)

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Basic

Cited by

1 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceFiberBundleVectorBundleContMDiffVectorBundleMemTrivializationAtlasMemTrivializationAtlas