Theorems · Theorem · functional analysis

ContinuousMultilinearMap.mkPiRing_apply_one_eq_self

∀ {R : Type u} {ι : Type v} {M : Type u_1} [inst : Fintype ι] [inst_1 : CommRing R] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] [inst_4 : TopologicalSpace R] [inst_5 : TopologicalSpace M] [inst_6 : ContinuousMul R]
  [inst_7 : ContinuousSMul R M] (f : ContinuousMultilinearMap R (fun x => R) M),
  ContinuousMultilinearMap.mkPiRing R ι (f fun x => 1) = f

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeCommRingAddCommMonoidModuleTopologicalSpaceTopologicalSpaceContinuousMulContinuousSMul