{"schema":"vela.problem-packet.v0.1","problem":1042,"statement":"Let $F\\subset\\mathbb{C}$ be a closed set of transfinite diameter $1$ which is not contained in any closed disc of radius $1$. If $f(z)=\\prod_{i=1}^n(z-z_i)\\in\\mathbb{C}[x]$ with all $z_i\\in F$ then can\\[\\{ z: \\lvert f(z)\\rvert < 1\\}\\]have $n$ connected components?If the transfinite diameter of $F$ is $<1$ then must this set only have at most $(1-c)n$ connected components, where $c>0$ depends only on $F$ (or just the transfinite diameter of $F$)?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}