Theorems · Definition · functional analysis

ContinuousMultilinearMap.mkPiRing

(R : Type u) →
  (ι : Type v) →
    {M : Type u_1} →
      [Fintype ι] →
        [inst : CommRing R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : Module R M] →
              [inst_3 : TopologicalSpace R] →
                [inst_4 : TopologicalSpace M] →
                  [ContinuousMul R] → [ContinuousSMul R M] → M → ContinuousMultilinearMap R (fun x => R) M

The canonical continuous multilinear map on R^ι, associating to m the product of all the m i (multiplied by a fixed reference element z in the target module)

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

11 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeCommRingAddCommMonoidModuleTopologicalSpaceTopologicalSpaceContinuousMulContinuousSMul