Theorems · Definition · algebraic topology

VectorBundle.continuousLinearEquivAt

(R : Type u_1) →
  {B : Type u_2} →
    (F : Type u_3) →
      (E : B → Type u_4) →
        [inst : NontriviallyNormedField R] →
          [inst_1 : (x : B) → AddCommMonoid (E x)] →
            [inst_2 : (x : B) → Module R (E x)] →
              [inst_3 : NormedAddCommGroup F] →
                [inst_4 : NormedSpace R F] →
                  [inst_5 : TopologicalSpace B] →
                    [inst_6 : TopologicalSpace (Bundle.TotalSpace F E)] →
                      [inst_7 : (x : B) → TopologicalSpace (E x)] →
                        [inst_8 : FiberBundle F E] → [VectorBundle R F E] → (b : B) → E b ≃L[R] F

A continuous linear equivalence between the fiber at b and the model fiber, induced by the preferred trivialisation at each b.

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

4 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceFiberBundleVectorBundle