Theorems · Theorem · algebraic topology

VectorBundleCore.trivializationAt_coordChange_eq

∀ {R : Type u_1} {B : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField R] [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace R F] [inst_3 : TopologicalSpace B] {ι : Type u_5} (Z : VectorBundleCore R B F ι) {b₀ b₁ b : B},
  b ∈ (trivializationAt F Z.Fiber b₀).baseSet ∩ (trivializationAt F Z.Fiber b₁).baseSet →
    ∀ (v : F),
      (Bundle.Trivialization.coordChangeL R (trivializationAt F Z.Fiber b₀) (trivializationAt F Z.Fiber b₁) b) v =
        (Z.coordChange (Z.indexAt b₀) (Z.indexAt b₁) b) v

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

0 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpace