Theorems · Theorem · functional analysis

LinearMap.antilipschitz_of_comap_nhds_le

∀ {𝕜 : Type u_1} {𝕜₂ : Type u_3} {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : NontriviallyNormedField 𝕜₂]
  [inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [h : RingHomIsometric σ₁₂] (f : E →ₛₗ[σ₁₂] F),
  Filter.comap (⇑f) (nhds 0) ≤ nhds 0 → ∃ K, AntilipschitzWith K ⇑f

Defined in

Mathlib.Analysis.Normed.Operator.NormedSpace

Cited by

1 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNontriviallyNormedFieldNontriviallyNormedFieldNormedSpaceNormedSpaceRingHomIsometric