Theorems · Definition · functional analysis

ContinuousAlternatingMap.compContinuousLinearMap

{R : Type u_1} →
  {M : Type u_2} →
    {M' : Type u_3} →
      {N : Type u_4} →
        {ι : Type u_6} →
          [inst : Semiring R] →
            [inst_1 : AddCommMonoid M] →
              [inst_2 : Module R M] →
                [inst_3 : TopologicalSpace M] →
                  [inst_4 : AddCommMonoid M'] →
                    [inst_5 : Module R M'] →
                      [inst_6 : TopologicalSpace M'] →
                        [inst_7 : AddCommMonoid N] →
                          [inst_8 : Module R N] →
                            [inst_9 : TopologicalSpace N] → M [⋀^ι]→L[R] N → (M' →L[R] M) → M' [⋀^ι]→L[R] N

If g is continuous alternating and f is a continuous linear map, then g (f m₁, ..., f mₙ) is again a continuous alternating map, that we call g.compContinuousLinearMap f.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Basic

Cited by

24 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpace