Theorems · Definition · functional analysis

ContinuousLinearMap.coprod

{R : Type u_1} →
  {M : Type u_3} →
    {M₁ : Type u_5} →
      {M₂ : Type u_6} →
        [inst : Semiring R] →
          [inst_1 : TopologicalSpace M] →
            [inst_2 : TopologicalSpace M₁] →
              [inst_3 : TopologicalSpace M₂] →
                [inst_4 : AddCommMonoid M] →
                  [inst_5 : Module R M] →
                    [ContinuousAdd M] →
                      [inst_7 : AddCommMonoid M₁] →
                        [inst_8 : Module R M₁] →
                          [inst_9 : AddCommMonoid M₂] →
                            [inst_10 : Module R M₂] → (M₁ →L[R] M) → (M₂ →L[R] M) → M₁ × M₂ →L[R] M

The continuous linear map given by (x, y) ↦ f₁ x + f₂ y.

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd

Cited by

24 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceTopologicalSpaceAddCommMonoidModuleContinuousAddAddCommMonoidModuleAddCommMonoidModule