Theorems · Theorem · algebraic topology

VectorPrebundle.mk_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} (he : e ∈ a.pretrivializationAtlas)
  (he' : e' ∈ a.pretrivializationAtlas) {b : B},
  b ∈ e.baseSet ∩ e'.baseSet →
    ∀ (v : F), (b, (VectorPrebundle.contMDiffCoordChange n IB a he he' b) v) = ↑e' ⟨b, e.symm b v⟩

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Basic

Cited by

0 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceVectorPrebundle.IsContMDiff