Theorems · Definition · functional analysis

ContinuousLinearMap.fromCompletion

{α : Type u_1} →
  {β : Type u_2} →
    {R₁ : Type u_3} →
      {R₂ : Type u_4} →
        [inst : UniformSpace α] →
          [inst_1 : AddCommGroup α] →
            [inst_2 : IsUniformAddGroup α] →
              [inst_3 : Semiring R₁] →
                [inst_4 : Module R₁ α] →
                  [inst_5 : UniformContinuousConstSMul R₁ α] →
                    [inst_6 : Semiring R₂] →
                      [inst_7 : UniformSpace β] →
                        [inst_8 : AddCommGroup β] →
                          [IsUniformAddGroup β] →
                            [inst_10 : Module R₂ β] →
                              [UniformContinuousConstSMul R₂ β] →
                                {σ : R₁ →+* R₂} →
                                  [T0Space β] → [CompleteSpace β] → (α →SL[σ] β) → UniformSpace.Completion α →SL[σ] β

Extension of a linear function to a linear function over the completion. This is the continuous linear version of UniformSpace.Completion.extension.

Defined in

Mathlib.Topology.Algebra.LinearMapCompletion

Cited by

5 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddCommGroupIsUniformAddGroupSemiringModuleUniformContinuousConstSMulSemiringUniformSpaceAddCommGroupIsUniformAddGroupModuleUniformContinuousConstSMulT0SpaceCompleteSpace