Theorems · Theorem · functional analysis

PointwiseConvergenceCLM.tendsto_nhds_atTop

∀ {α : Type u_1} {𝕜₁ : Type u_3} {𝕜₂ : Type u_4} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂] {σ : 𝕜₁ →+* 𝕜₂}
  {E : Type u_7} {F : Type u_8} [inst_2 : AddCommGroup E] [inst_3 : TopologicalSpace E] [inst_4 : Module 𝕜₁ E]
  [inst_5 : NormedAddCommGroup F] [inst_6 : NormedSpace 𝕜₂ F] [inst_7 : SemilatticeSup α] [Nonempty α]
  (u : α → E →SLₚₜ[σ] F) (y₀ : E →SLₚₜ[σ] F),
  Filter.Tendsto u Filter.atTop (nhds y₀) ↔ ∀ (x : E) (ε : ℝ), 0 < ε → ∃ k₀, ∀ (k : α), k₀ ≤ k → ‖(u k) x - y₀ x‖ < ε

Defined in

Mathlib.Analysis.LocallyConvex.PointwiseConvergence

Cited by

0 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupTopologicalSpaceModuleNormedAddCommGroupNormedSpaceSemilatticeSupNonempty