Theorems · Theorem · global analysis

Bundle.Trivialization.mdifferentiable

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_12} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_13} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {F : Type u_14}
  [inst_4 : NormedAddCommGroup F] [inst_5 : NormedSpace 𝕜 F] {M : Type u_15} [inst_6 : TopologicalSpace M]
  [inst_7 : ChartedSpace H M] (Z : M → Type u_16) [inst_8 : TopologicalSpace (Bundle.TotalSpace F Z)]
  [inst_9 : (b : M) → TopologicalSpace (Z b)] [inst_10 : FiberBundle F Z] [inst_11 : (b : M) → AddCommMonoid (Z b)]
  [inst_12 : (b : M) → Module 𝕜 (Z b)] [inst_13 : VectorBundle 𝕜 F Z] [ContMDiffVectorBundle 1 F Z I]
  (e : Bundle.Trivialization F Bundle.TotalSpace.proj) [MemTrivializationAtlas e],
  OpenPartialHomeomorph.MDifferentiable (I.prod (modelWithCornersSelf 𝕜 F)) (I.prod (modelWithCornersSelf 𝕜 F))
    e.toOpenPartialHomeomorph

Defined in

Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable

Cited by

1 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceTopologicalSpaceFiberBundleAddCommMonoidModuleVectorBundleContMDiffVectorBundleMemTrivializationAtlas