Theorems · Theorem · global analysis

Bundle.Trivialization.isLocalFrameOn_localFrame_baseSet

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {F : Type u_5} [inst_6 : NormedAddCommGroup F]
  [inst_7 : NormedSpace 𝕜 F] (n : WithTop ℕ∞) {V : M → Type u_6} [inst_8 : TopologicalSpace (Bundle.TotalSpace F V)]
  [inst_9 : (x : M) → AddCommGroup (V x)] [inst_10 : (x : M) → Module 𝕜 (V x)]
  [inst_11 : (x : M) → TopologicalSpace (V x)] [inst_12 : FiberBundle F V] [inst_13 : VectorBundle 𝕜 F V]
  [ContMDiffVectorBundle n F V I] {ι : Type u_7} (e : Bundle.Trivialization F Bundle.TotalSpace.proj)
  [inst_15 : MemTrivializationAtlas e] (b : Module.Basis ι 𝕜 F), IsLocalFrameOn I F n (e.localFrame b) e.baseSet

b.localFrame e i is indeed a local frame on e.baseSet

Defined in

Mathlib.Geometry.Manifold.VectorBundle.LocalFrame

Cited by

7 results in Mathlib

Foundations

Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceAddCommGroupModuleTopologicalSpaceFiberBundleVectorBundleContMDiffVectorBundleMemTrivializationAtlas