Theorems · Definition · algebraic topology

VectorPrebundle.coordChange

{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 : (x : B) → TopologicalSpace (E x)] →
                      (a : VectorPrebundle R F E) →
                        {e e' : Bundle.Pretrivialization F Bundle.TotalSpace.proj} →
                          e ∈ a.pretrivializationAtlas → e' ∈ a.pretrivializationAtlas → B → F →L[R] F

A randomly chosen coordinate change on a VectorPrebundle, given by the field exists_coordChange.

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

3 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace