Theorems · Inductive type · Lie groups

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] →
              ModelWithCorners 𝕜 E H →
                WithTop ℕ∞ → (G : Type u_4) → [Group G] → [inst : TopologicalSpace G] → [ChartedSpace H G] → Prop

A (multiplicative) Lie group is a group and a C^n manifold at the same time in which the multiplication and inverse operations are C^n.

Defined in

Mathlib.Geometry.Manifold.Algebra.LieGroup

Cited by

22 results in Mathlib

Foundations

Depth 12 from the axioms · uses no axioms

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceGroupTopologicalSpaceChartedSpace