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  "body": "\n## Summary\n\nA Riemann domain over $\\C^n$ is a connected space that lies over $\\C^n$ through a [[local homeomorphism|MDH71ZZ8XX]], possibly with several sheets over the same point.\nIt is the several-variable analogue of a Riemann surface spread over the plane.\nRiemann domains are needed because analytic continuation of a holomorphic function can lead to several values over one point.\nThe envelope of holomorphy of a domain in $\\C^n$ is in general a Riemann domain and not a subset of $\\C^n$.\n\n## Explanations\n\n### L1 human\n\nImagine several transparent copies of a region of $\\C^n$, stacked on top of each other and glued along some cuts, like a spiral staircase.\nOver each point of $\\C^n$ there may be several points of the staircase, but near each of its points the staircase looks exactly like an open set of $\\C^n$.\nFor example, the map $(w, z_2) \\mapsto (e^w, z_2)$ from $\\C^2$ to $\\C^2$ makes $\\C^2$ into a Riemann domain over $\\C^2$ with infinitely many sheets over each point with $z_1 \\ne 0$.\nOn this domain the logarithm of $z_1$ becomes a single-valued function, namely $w$.\n",
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