Theorems · Definition · global analysis

smoothRightMul

{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) →
                {G : Type u_4} →
                  [inst_4 : Mul G] →
                    [inst_5 : TopologicalSpace G] →
                      [inst_6 : ChartedSpace H G] → G → [ContMDiffMul I (↑⊤) G] → ContMDiffMap I I G G ↑⊤

Right multiplication by g. It is meant to mimic the usual notation in Lie groups. Used mostly through the notation 𝑹. Lemmas involving smoothRightMul with the notation 𝑹 usually use R instead of 𝑹 in the names.

Defined in

Mathlib.Geometry.Manifold.Algebra.Monoid

Cited by

4 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceMulTopologicalSpaceChartedSpaceContMDiffMul