Theorems · Theorem · functional analysis

SchauderBasis.tendsto_proj

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X] (b : SchauderBasis 𝕜 X) (x : X),
  Filter.Tendsto (fun n => (b.proj n) x) Filter.atTop (nhds x)

The projections converge pointwise to the identity map.

Defined in

Mathlib.Analysis.Normed.Module.Bases

Cited by

1 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace