Theorems · Inductive type · global analysis

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

Basic hypothesis to talk about a C^n (Lie) monoid or a C^n semigroup. A C^n monoid over G, for example, is obtained by requiring both the instances Monoid G and ContMDiffMul I n G. See also ContMDiffSMul I I' n G M for C^n actions of G on a manifold M.

Defined in

Mathlib.Geometry.Manifold.Algebra.Monoid

Cited by

99 results in Mathlib

Foundations

Depth 12 from the axioms, rests on 76 definitions · uses no axioms

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceMulTopologicalSpaceChartedSpace