Theorems · Theorem · functional analysis

ContinuousMultilinearMap.alternatization_apply_apply

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} {ι : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : TopologicalSpace M] [inst_4 : AddCommGroup N] [inst_5 : Module R N]
  [inst_6 : TopologicalSpace N] [inst_7 : IsTopologicalAddGroup N] [inst_8 : Fintype ι] [inst_9 : DecidableEq ι]
  (f : ContinuousMultilinearMap R (fun x => M) N) (v : ι → M),
  (ContinuousMultilinearMap.alternatization f) v = ∑ σ, Equiv.Perm.sign σ • f (v ∘ ⇑σ)

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Basic

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupFintypeDecidableEq