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  "body": "\n## Summary\n\nThe disk algebra $A(\\mathbb{D})$ is the algebra of continuous functions on the closed unit disc that are holomorphic inside it.\nWith the supremum norm it is a commutative Banach algebra, and the polynomials are dense in it.\nIt is the basic example of a uniform algebra and a natural setting for boundary problems on the [[unit disc|8G5ABXRK85]].\n\n## Explanations\n\n### L1 human\n\nTake a function on the closed disc that is continuous up to the edge and holomorphic in the interior.\nSuch functions can be added and multiplied, and uniform limits of them have the same properties.\nPolynomials are examples, and every element is a uniform limit of polynomials.\nThe function $\\sum_{n \\ge 1} z^n / n^2$ is in the disk algebra, since the series converges uniformly on the closed disc.\nThe function $1/(1 - z)$ is holomorphic in the open disc but does not belong, because it is unbounded near $1$.\n",
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