= Polynomial hull
{title2=$\widehat K=\{z:|p(z)|\leq\sup_K|p|\text{ for every polynomial }p\}$}
For a compact set $K\subset\mathbb C^n$, its polynomial hull is the set displayed, where $p$ ranges over all complex <multivariate polynomials>. It contains $K$. In one complex dimension, bounded complementary components are filled in: the <maximum modulus principle> bounds every <polynomial> inside those components by its boundary values. Polynomial approximation and separation distinguish points outside the hull.
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