Theorems · Definition · global analysis

mvfderivWithin

{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] →
              (I : ModelWithCorners 𝕜 E H) →
                {M : Type u_4} →
                  [inst_4 : TopologicalSpace M] →
                    [inst_5 : ChartedSpace H M] →
                      {F : Type u_8} →
                        [inst_6 : NormedAddCommGroup F] →
                          [inst_7 : NormedSpace 𝕜 F] → (M → F) → Set M → (x : M) → TangentSpace I x →L[𝕜] F

mvfderivWithin I J f s x is the mfderiv of a vector-valued function f on M at x within the set s, but taking values in the target normed space directly. The difference to mfderivWithin is explained in the module-docstring for Mathlib/Geometry/Manifold/MFDeriv/NormedSpace.lean. Future: this could be generalised to functions into additive torsors over abelian Lie groups.

Defined in

Mathlib.Geometry.Manifold.MFDeriv.NormedSpace

Cited by

22 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpace