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  "body": "\n## Summary\n\nThe Whitney $C^\\infty$ topology, also called the strong $C^\\infty$ topology, is a topology on the set $C^\\infty(M, N)$ of smooth maps between [[smooth manifolds|F45VQ47GPV]].\nTwo maps are close in it when their values and derivatives up to some order are close at every point.\nThe allowed error may shrink towards infinity.\nIt is the standard topology in which one says that a property of maps is generic, stable or open.\nWith it, $C^\\infty(M, N)$ is a [[Baire space|0ZH5AJ2ED7]], which makes transversality arguments work.\n\n## Explanations\n\n### L1 human\n\nThink of a smooth function on the real line and draw a thin tube around its graph.\nThe tube may get thinner and thinner far out, like the function $1/(1 + x^2)$.\nIn the Whitney topology, the functions whose graphs stay inside such a tube form a neighbourhood, and one can ask the same of the derivatives.\nSo the constant function $1/n$ is never close to $0$ in this topology, however large $n$ is: far out, the tube around $0$ is thinner than $1/n$.\nThis strict control at infinity is what makes many sets of nice maps open.\n",
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