Theorems · Definition · global analysis

Derivation.evalAt

{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] →
                      (x : M) →
                        Derivation 𝕜 (ContMDiffMap I (modelWithCornersSelf 𝕜 𝕜) M 𝕜 ↑⊤)
                            (ContMDiffMap I (modelWithCornersSelf 𝕜 𝕜) M 𝕜 ↑⊤) →ₗ[PointedContMDiffMap 𝕜 I M (↑⊤) x]
                          PointDerivation I x

The evaluation at a point as a linear map.

Defined in

Mathlib.Geometry.Manifold.DerivationBundle

Cited by

8 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace