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erdos_509.variants.Pommerenke_connected

Specification

Let $f(z) ∈ ℂ[z]$ be a monic non-constant polynomial. If it is connected, can the set $\{z ∈ ℂ : |f(z)| ≤ 1\}$ be covered by a set of circles the sum of whose radii is $≤ 2$? Solution: True. This is due to Pommerenke.

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Lean 4 Statement 
theorem erdos_509.variants.Pommerenke_connected : answer(True) ↔ ∀ (f : ℂ[X]), f.Monic → f.natDegree ≠ 0 →
    IsConnected {z | ‖f.eval z‖ ≤ 1} →
    ∃ (ι : Type), Nonempty (BoundedDiscCover {z | ‖f.eval z‖ ≤ 1} 2 ι)
ID: ErdosProblems__509__erdos_509.variants.Pommerenke_connected
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