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  "body": "\n## Summary\n\nA ringed space is a topological space together with a sheaf of commutative rings on it.\nThe rings play the role of the rings of functions on the open sets.\nManifolds with their smooth functions, complex manifolds with their holomorphic functions, and varieties with their regular functions are all ringed spaces.\nSchemes are defined as ringed spaces of a special kind, so the notion is the starting point of modern algebraic geometry.\n\n## Explanations\n\n### L1 human\n\nMany kinds of geometry fix a space and say which functions on it are allowed: continuous, smooth, holomorphic or polynomial.\nA ringed space packages exactly this: a space, and for each open set a ring of allowed functions on it.\nFor example, $\\R^n$ with the smooth functions on each open set is a ringed space.\nThe point of view lets one compare different geometries in one framework, and it allows \"functions\" that are not functions on points at all, as in scheme theory.\n",
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