Theorems · Definition · functional analysis

ContinuousLinearEquiv.smulLeft

{R₁ : Type u_1} →
  [inst : Semiring R₁] →
    {M₁ : Type u_4} →
      [inst_1 : TopologicalSpace M₁] →
        [inst_2 : AddCommMonoid M₁] →
          [inst_3 : Module R₁ M₁] →
            {G : Type u_9} →
              [inst_4 : Group G] →
                [inst_5 : DistribMulAction G M₁] →
                  [ContinuousConstSMul G M₁] → [SMulCommClass G R₁ M₁] → G →* M₁ ≃L[R₁] M₁

Scalar multiplication by a group element as a continuous linear equivalence.

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

6 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceAddCommMonoidModuleGroupDistribMulActionContinuousConstSMulSMulCommClass