Theorems · Theorem · functional analysis

ContinuousLinearMap.completion_apply_coe

∀ {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]
  [inst_9 : IsUniformAddGroup β] [inst_10 : Module R₂ β] [inst_11 : UniformContinuousConstSMul R₂ β] {σ : R₁ →+* R₂}
  (f : α →SL[σ] β) (a : α), f.completion ↑a = ↑(f a)

Defined in

Mathlib.Topology.Algebra.LinearMapCompletion

Cited by

1 results in Mathlib

Foundations

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

Assumes

UniformSpaceAddCommGroupIsUniformAddGroupSemiringModuleUniformContinuousConstSMulSemiringUniformSpaceAddCommGroupIsUniformAddGroupModuleUniformContinuousConstSMul