Theorems · Theorem · algebraic topology

Bundle.Trivialization.IsLinear.linear

∀ {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 : Bundle.Trivialization F Bundle.TotalSpace.proj} [self : Bundle.Trivialization.IsLinear R e],
  ∀ b ∈ e.baseSet, IsLinearMap R fun x => (↑e ⟨b, x⟩).2

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Bundle.Trivialization.IsLinear