Theorems · Definition · functional analysis

ContinuousAlternatingMap.apply

(𝕜 : Type u_1) →
  (E : Type u_2) →
    (F : Type u_3) →
      {ι : Type u_4} →
        [inst : NormedField 𝕜] →
          [inst_1 : AddCommGroup E] →
            [inst_2 : Module 𝕜 E] →
              [inst_3 : TopologicalSpace E] →
                [inst_4 : AddCommGroup F] →
                  [inst_5 : Module 𝕜 F] →
                    [inst_6 : TopologicalSpace F] →
                      [inst_7 : IsTopologicalAddGroup F] →
                        [inst_8 : ContinuousConstSMul 𝕜 F] → [ContinuousSMul 𝕜 E] → (ι → E) → E [⋀^ι]→L[𝕜] F →L[𝕜] F

The application of a multilinear map as a ContinuousLinearMap.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Topology

Cited by

12 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMulContinuousSMul