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  "body": "\n## Summary\n\nA Banach manifold is a space that looks locally like an open subset of a Banach space, with smooth changes of coordinates.\nIt extends the notion of a smooth manifold to infinite dimension.\nSpaces of maps, of curves or of operators often carry such a structure.\nCalculus on Banach manifolds works much as in finite dimension, because the inverse function theorem holds in Banach spaces.\n\n## Explanations\n\n### L1 human\n\nA surface is built from patches, each of which looks like a piece of the plane.\nA Banach manifold is built from patches that look like pieces of a Banach space, which may be a space of functions.\nThe patches are glued by maps that can be differentiated.\nFor example, the unit sphere of the Hilbert space $\\ell^2$ is a Banach manifold, and its patches are pieces of a hyperplane in $\\ell^2$.\n",
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