Theorems · Theorem · Lie groups

contMDiff_neg

∀ {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 : TopologicalSpace G] [inst_5 : ChartedSpace H G] [inst_6 : AddGroup G] [LieAddGroup I n G],
  ContMDiff I I n fun x => -x

In an additive Lie group, inversion is a smooth map.

Defined in

Mathlib.Geometry.Manifold.Algebra.LieGroup

Cited by

2 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceAddGroupLieAddGroup