Theorems · Definition · global analysis

ContMDiffMap.comp

{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'] →
                        {I : ModelWithCorners 𝕜 E H} →
                          {I' : ModelWithCorners 𝕜 E' H'} →
                            {M : Type u_6} →
                              [inst_7 : TopologicalSpace M] →
                                [inst_8 : ChartedSpace H M] →
                                  {M' : Type u_7} →
                                    [inst_9 : TopologicalSpace M'] →
                                      [inst_10 : ChartedSpace H' M'] →
                                        {E'' : Type u_8} →
                                          [inst_11 : NormedAddCommGroup E''] →
                                            [inst_12 : NormedSpace 𝕜 E''] →
                                              {H'' : Type u_9} →
                                                [inst_13 : TopologicalSpace H''] →
                                                  {I'' : ModelWithCorners 𝕜 E'' H''} →
                                                    {M'' : Type u_10} →
                                                      [inst_14 : TopologicalSpace M''] →
                                                        [inst_15 : ChartedSpace H'' M''] →
                                                          {n : WithTop ℕ∞} →
                                                            ContMDiffMap I' I'' M' M'' n →
                                                              ContMDiffMap I I' M M' n → ContMDiffMap I I'' M M'' n

The composition of C^n maps, as a C^n map.

Defined in

Mathlib.Geometry.Manifold.ContMDiffMap

Cited by

11 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace