Theorems · Definition · global analysis

ContMDiffMap

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {E' : Type u_3} →
            [inst_3 : NormedAddCommGroup E'] →
              [inst_4 : NormedSpace 𝕜 E'] →
                {H : Type u_4} →
                  [inst_5 : TopologicalSpace H] →
                    {H' : Type u_5} →
                      [inst_6 : TopologicalSpace H'] →
                        ModelWithCorners 𝕜 E H →
                          ModelWithCorners 𝕜 E' H' →
                            (M : Type u_6) →
                              [inst : TopologicalSpace M] →
                                [ChartedSpace H M] →
                                  (M' : Type u_7) →
                                    [inst : TopologicalSpace M'] →
                                      [ChartedSpace H' M'] → WithTop ℕ∞ → Type (max 0 u_6 u_7)

Bundled n times continuously differentiable maps, denoted as C^n(I, M; I', M') and C^n(I, M; k) (when the target is a normed space k with the trivial model) in the Manifold namespace.

Defined in

Mathlib.Geometry.Manifold.ContMDiffMap

Cited by

125 results in Mathlib

Foundations

Depth 176 from the axioms, rests on 4,288 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace