Theorems · Theorem · functional analysis

ContinuousLinearMap.prod_ext_iff

∀ {R : Type u_1} [inst : Semiring R] {M : Type u_2} [inst_1 : TopologicalSpace M] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] {M₂ : Type u_3} [inst_4 : TopologicalSpace M₂] [inst_5 : AddCommMonoid M₂]
  [inst_6 : Module R M₂] {M₃ : Type u_4} [inst_7 : TopologicalSpace M₃] [inst_8 : AddCommMonoid M₃]
  [inst_9 : Module R M₃] {f g : M × M₂ →L[R] M₃},
  f = g ↔
    f ∘SL ContinuousLinearMap.inl R M M₂ = g ∘SL ContinuousLinearMap.inl R M M₂ ∧
      f ∘SL ContinuousLinearMap.inr R M M₂ = g ∘SL ContinuousLinearMap.inr R M M₂

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd

Cited by

1 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModule