Let $f\in \mathbb{C}[x]$ be a monic polynomial with $m$ distinct roots, and let $c>0$ be a constant small enough such that $\{ z: \lvert f(z)\rvert\leq c\}$ has $m$ distinct connected components.

1False ↔2  ∀ (f : Polynomial ℂ) (m : ℕ) (c : ℝ),3    f.Monic →4      (f.rootSet ℂ).ncard = m →5        0 < c →6          (Erdos1047.componentsIn (Erdos1047.sublevelSet f c)).ncard = m →7            ∀ t ∈ Erdos1047.componentsIn (Erdos1047.sublevelSet f c), Convex ℝ t