Theorems · Theorem · algebraic topology

FiberBundle.writtenInExtChartAt_trivializationAt

∀ {𝕜 : Type u_1} {B : Type u_2} {F : Type u_4} {E : B → Type u_6} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace 𝕜 F] [inst_3 : TopologicalSpace (Bundle.TotalSpace F E)]
  [inst_4 : (x : B) → TopologicalSpace (E x)] {EB : Type u_7} [inst_5 : NormedAddCommGroup EB]
  [inst_6 : NormedSpace 𝕜 EB] {HB : Type u_8} [inst_7 : TopologicalSpace HB] {IB : ModelWithCorners 𝕜 EB HB}
  [inst_8 : TopologicalSpace B] [inst_9 : ChartedSpace HB B] [inst_10 : FiberBundle F E] {x : Bundle.TotalSpace F E}
  {y : EB × F},
  y ∈ (extChartAt (IB.prod (modelWithCornersSelf 𝕜 F)) x).target →
    writtenInExtChartAt (IB.prod (modelWithCornersSelf 𝕜 F)) (IB.prod (modelWithCornersSelf 𝕜 F)) x
        (↑(trivializationAt F E x.proj)) y =
      y

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Basic

Cited by

0 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiberBundle