Theorems · Definition · functional analysis

ContinuousAlternatingMap.smulRight

{R : Type u_1} →
  {M : Type u_2} →
    {N : Type u_3} →
      {ι : Type u_4} →
        [inst : CommSemiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : AddCommMonoid N] →
              [inst_3 : Module R M] →
                [inst_4 : Module R N] →
                  [inst_5 : TopologicalSpace R] →
                    [inst_6 : TopologicalSpace M] →
                      [inst_7 : TopologicalSpace N] → [ContinuousSMul R N] → M [⋀^ι]→L[R] R → N → M [⋀^ι]→L[R] N

Given a continuous R-alternating map f taking values in R, f.smulRight z is the continuous alternating map sending m to f m • z.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Basic

Cited by

2 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleTopologicalSpaceTopologicalSpaceTopologicalSpaceContinuousSMul