Theorems · Theorem · global analysis

continuousMul_of_contMDiffMul

∀ {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) (n : WithTop ℕ∞)
  {G : Type u_4} [inst_4 : Mul G] [inst_5 : TopologicalSpace G] [inst_6 : ChartedSpace H G] [ContMDiffMul I n G],
  ContinuousMul G

If the multiplication is C^n, then it is continuous. This is not an instance for technical reasons, see note [Design choices about smooth algebraic structures].

Defined in

Mathlib.Geometry.Manifold.Algebra.Monoid

Cited by

2 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceMulTopologicalSpaceChartedSpaceContMDiffMul