Mergelyan's theorem with zero-free polynomials

Decide whether functions holomorphic and zero-free inside a compact set can be uniformly approximated by polynomials with no zeros on the set.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"analysis",
5	"number-theory"
6	],
7	"type": "proof",
8	"source": {
9	"key": "aimpl",
10	"name": "AIM Problem Lists",
11	"url": "http://aimpl.org/hyperbolicpoly/9/",
12	"id": "hyperbolicpoly 9.1",
13	"curator": "American Institute of Mathematics",
14	"poser": "Paul Gauthier",
15	"status": "open",
16	"as_of": "2026-10-20",
17	"catalog": "0521c19bbd38"
18	},
19	"review": true,
20	"approval": "first-time"
21	}