Theorems · Definition · global analysis

ContMDiffMap.restrictRingHom

{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] →
                    (I : ModelWithCorners 𝕜 E H) →
                      {H' : Type u_5} →
                        [inst_6 : TopologicalSpace H'] →
                          (I' : ModelWithCorners 𝕜 E' H') →
                            {N : Type u_6} →
                              [inst_7 : TopologicalSpace N] →
                                [inst_8 : ChartedSpace H N] →
                                  {n : WithTop ℕ∞} →
                                    (R : Type u_10) →
                                      [inst_9 : Ring R] →
                                        [inst_10 : TopologicalSpace R] →
                                          [inst_11 : ChartedSpace H' R] →
                                            [inst_12 : ContMDiffRing I' n R] →
                                              {U V : TopologicalSpace.Opens N} →
                                                U ≤ V → ContMDiffMap I I' (↥V) R n →+* ContMDiffMap I I' (↥U) R n

For a "C^n ring" R and open sets U ⊆ V in N, the "restriction" ring homomorphism from C^n⟮I, V; I', R⟯ to C^n⟮I, U; I', R⟯.

Defined in

Mathlib.Geometry.Manifold.Algebra.SmoothFunctions

Cited by

1 results in Mathlib

Foundations

Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceRingTopologicalSpaceChartedSpaceContMDiffRing