Theorems · Theorem · functional analysis

LinearIndependent.eventually

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type v} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [CompleteSpace 𝕜] {ι : Type u_1} [Finite ι] {f : ι → E},
  LinearIndependent 𝕜 f → ∀ᶠ (g : ι → E) in nhds f, LinearIndependent 𝕜 g

Defined in

Mathlib.Analysis.Normed.Module.FiniteDimension

Cited by

1 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpaceFinite