Theorems · Inductive type · algebraic topology

VectorBundle

(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)] →
            [(x : B) → Module R (E x)] →
              [inst_3 : NormedAddCommGroup F] →
                [NormedSpace R F] →
                  [inst : TopologicalSpace B] →
                    [inst_4 : TopologicalSpace (Bundle.TotalSpace F E)] →
                      [inst_5 : (x : B) → TopologicalSpace (E x)] → [FiberBundle F E] → Prop

The space Bundle.TotalSpace F E (for E : B → Type* such that each E x is a topological vector space) has a topological vector space structure with fiber F (denoted with VectorBundle R F E) if around every point there is a fiber bundle trivialization which is linear in the fibers.

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

315 results in Mathlib

Foundations

Depth 45 from the axioms, rests on 427 definitions · uses propext, Quot.sound

Assumes

NontriviallyNormedFieldAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceFiberBundle