Theorems · Inductive type · global analysis

IsLocalFrameOn

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type u_3} →
            [inst_3 : TopologicalSpace H] →
              ModelWithCorners 𝕜 E H →
                {M : Type u_4} →
                  [inst_4 : TopologicalSpace M] →
                    [ChartedSpace H M] →
                      (F : Type u_5) →
                        [inst_6 : NormedAddCommGroup F] →
                          [NormedSpace 𝕜 F] →
                            {V : M → Type u_6} →
                              [inst_8 : TopologicalSpace (Bundle.TotalSpace F V)] →
                                [inst_9 : (x : M) → AddCommGroup (V x)] →
                                  [(x : M) → Module 𝕜 (V x)] →
                                    [inst : (x : M) → TopologicalSpace (V x)] →
                                      [FiberBundle F V] →
                                        {ι : Type u_7} → WithTop ℕ∞ → (ι → (x : M) → V x) → Set M → Prop

A family of sections s i of V → M is called a C^k local frame on a set U ⊆ M iff - the section values s i x form a basis for each x ∈ U, - each section s i is C^k on U.

Defined in

Mathlib.Geometry.Manifold.VectorBundle.LocalFrame

Cited by

25 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceAddCommGroupModuleTopologicalSpaceFiberBundle