Theorems · Theorem · algebraic topology

Bundle.Pretrivialization.coe_linearMapAt

∀ {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 : AddCommMonoid F] [inst_4 : Module R F]
  [inst_5 : (x : B) → AddCommMonoid (E x)] [inst_6 : (x : B) → Module R (E x)]
  (e : Bundle.Pretrivialization F Bundle.TotalSpace.proj) [inst_7 : Bundle.Pretrivialization.IsLinear R e] (b : B),
  ⇑(Bundle.Pretrivialization.linearMapAt R e b) = fun y => if b ∈ e.baseSet then (↑e ⟨b, y⟩).2 else 0

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

3 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceAddCommMonoidModuleAddCommMonoidModuleBundle.Pretrivialization.IsLinear