Theorems · Theorem · Lie groups

topologicalGroup_of_lieGroup

∀ {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 : Group G] [LieGroup I n G],
  IsTopologicalGroup G

A Lie group is a topological group. This is not an instance for technical reasons, see note [Design choices about smooth algebraic structures].

Defined in

Mathlib.Geometry.Manifold.Algebra.LieGroup

Cited by

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Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceGroupLieGroup