Theorems · Theorem · algebraic topology

Bundle.Trivialization.coordChangeL_apply

∀ {R : Type u_1} {B : Type u_2} {F : Type u_3} {E : B → Type u_4} [inst : Semiring R] [inst_1 : TopologicalSpace F]
  [inst_2 : TopologicalSpace B] [inst_3 : TopologicalSpace (Bundle.TotalSpace F E)] [inst_4 : AddCommMonoid F]
  [inst_5 : Module R F] [inst_6 : (x : B) → AddCommMonoid (E x)] [inst_7 : (x : B) → Module R (E x)]
  (e e' : Bundle.Trivialization F Bundle.TotalSpace.proj) [inst_8 : Bundle.Trivialization.IsLinear R e]
  [inst_9 : Bundle.Trivialization.IsLinear R e'] {b : B},
  b ∈ e.baseSet ∩ e'.baseSet → ∀ (y : F), (Bundle.Trivialization.coordChangeL R e e' b) y = (↑e' ⟨b, e.symm b y⟩).2

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

8 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceTopologicalSpaceAddCommMonoidModuleAddCommMonoidModuleBundle.Trivialization.IsLinearBundle.Trivialization.IsLinear