Theorems · Theorem · global analysis

MulAction.contMDiffSMul_compHom

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {H' : Type u_4}
  [inst_4 : TopologicalSpace H'] {E' : Type u_5} [inst_5 : NormedAddCommGroup E'] [inst_6 : NormedSpace 𝕜 E']
  {I' : ModelWithCorners 𝕜 E' H'} {H'' : Type u_6} [inst_7 : TopologicalSpace H''] {E'' : Type u_7}
  [inst_8 : NormedAddCommGroup E''] [inst_9 : NormedSpace 𝕜 E''] {I'' : ModelWithCorners 𝕜 E'' H''} {G : Type u_8}
  [inst_10 : TopologicalSpace G] [inst_11 : ChartedSpace H G] {M : Type u_9} [inst_12 : TopologicalSpace M]
  [inst_13 : ChartedSpace H' M] [inst_14 : Monoid G] [inst_15 : MulAction G M] {n : WithTop ℕ∞}
  [ContMDiffSMul I I' n G M] {G' : Type u_11} [inst_17 : TopologicalSpace G'] [inst_18 : ChartedSpace H'' G']
  [inst_19 : Monoid G'] {f : G' →* G}, ContMDiff I'' I n ⇑f → ContMDiffSMul I'' I' n G' M

If an action is continuously differentiable, then post-composing this action with a continuously differentiable homomorphism gives again a continuously differentiable action.

Defined in

Mathlib.Geometry.Manifold.Algebra.SMul

Cited by

0 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceMonoidMulActionContMDiffSMulTopologicalSpaceChartedSpaceMonoid