Theorems · Theorem · algebraic topology

VectorBundleCore.localTriv_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) (i j : ι)
  {b : B},
  b ∈ (Z.localTriv i).baseSet ∧ b ∈ (Z.localTriv j).baseSet →
    ∀ (v : F), (Bundle.Trivialization.coordChangeL R (Z.localTriv i) (Z.localTriv j) b) v = (Z.coordChange i j b) v

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

1 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpace