Theorems · Theorem · functional analysis

LinearIsometry.isEmbedding

∀ {R : Type u_1} {R₂ : Type u_2} {E₂ : Type u_6} {F : Type u_9} [inst : Semiring R] [inst_1 : Semiring R₂]
  {σ₁₂ : R →+* R₂} [inst_2 : SeminormedAddCommGroup E₂] [inst_3 : Module R₂ E₂] [inst_4 : NormedAddCommGroup F]
  [inst_5 : Module R F] (f : F →ₛₗᵢ[σ₁₂] E₂), Topology.IsEmbedding ⇑f

Defined in

Mathlib.Analysis.Normed.Operator.LinearIsometry

Cited by

1 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSeminormedAddCommGroupModuleNormedAddCommGroupModule