Theorems · Definition · algebraic topology

Bundle.Trivialization.linearEquivAt

(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) →
                          [Bundle.Trivialization.IsLinear R e] → (b : B) → b ∈ e.baseSet → E b ≃ₗ[R] F

A trivialization for a vector bundle defines linear equivalences between the fibers and the model space.

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

9 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceTopologicalSpaceAddCommMonoidModuleAddCommMonoidModuleBundle.Trivialization.IsLinear