Theorems · Theorem · algebraic topology

Bundle.Trivialization.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)]
  (e : Bundle.Trivialization F Bundle.TotalSpace.proj) [inst_4 : AddCommMonoid F] [inst_5 : Module R F]
  [inst_6 : (x : B) → AddCommMonoid (E x)] [inst_7 : (x : B) → Module R (E x)] [Bundle.Trivialization.IsLinear R e]
  {b : B}, b ∈ e.baseSet → IsLinearMap R fun y => (↑e ⟨b, y⟩).2

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

6 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceTopologicalSpaceAddCommMonoidModuleAddCommMonoidModuleBundle.Trivialization.IsLinear