compContinuousLinearMap — Mathlib

English

If for every NNReal r the isBigO condition holds, then radius(p) = ∞.

Русский

Если для каждого NNReal r условие IsBigO выполняется, то radius(p) = ∞.

LaTeX

$$radius_eq_top_of_forall_nnreal_isBigO (λ r, IsBigO(atTop, (λ n, ‖p n‖ * (r : ℝ) ^ n)) (λ _ => 1))$$

Lean4

theorem compContinuousLinearMap (hf : AnalyticOnNhd 𝕜 f s) : AnalyticOnNhd 𝕜 (f ∘ u) (u ⁻¹' s) := fun x hx =>
  AnalyticAt.compContinuousLinearMap (hf (u x) hx)

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