Theorems · Theorem · functional analysis

ContinuousAlternatingMap.map_piecewise_add

∀ {R : Type u_1} {M : Type u_2} {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 N] [inst_5 : Module R N]
  [inst_6 : TopologicalSpace N] (f : M [⋀^ι]→L[R] N) [inst_7 : DecidableEq ι] (m m' : ι → M) (t : Finset ι),
  f (t.piecewise (m + m') m') = ∑ s ∈ t.powerset, f (s.piecewise m m')

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Basic

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceDecidableEq