hasBasis_nhds_zero — Mathlib

English

The UniformOnFun embedding across VonNBounded subsets yields a uniform embedding.

Русский

Единичное вложение UniformOnFun над VonNBounded подмножествами образует uniforme embedding.

LaTeX

$$$$ IsUniformEmbedding \left( f \mapsto UniformOnFun.ofFun \{s | Bornology.IsVonNBounded 𝕜_1 s\} f \right) $$$$

Lean4

protected theorem hasBasis_nhds_zero [TopologicalSpace F] [IsTopologicalAddGroup F] :
    (𝓝 (0 : E →SL[σ] F)).HasBasis (fun SV : Set E × Set F => IsVonNBounded 𝕜₁ SV.1 ∧ SV.2 ∈ (𝓝 0 : Filter F)) fun SV =>
      {f : E →SL[σ] F | ∀ x ∈ SV.1, f x ∈ SV.2} :=
  ContinuousLinearMap.hasBasis_nhds_zero_of_basis (𝓝 0).basis_sets

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