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  "body": "\n## Summary\n\nA surface is a [[topological manifold|QQQ9B1DK4P]] of dimension $2$: a space that looks like a piece of the plane near each of its points.\nSpheres, tori, the Möbius strip and the Klein bottle are surfaces.\nClosed surfaces are completely classified by orientability and Euler characteristic, see the [[classification of surfaces|2SFM73YET0]].\nSurfaces are the first nontrivial case of manifold topology and appear throughout geometry, complex analysis and dynamics.\n\n## Explanations\n\n### L1 human\n\nA surface is a space in which a tiny creature, looking around itself, would always believe it lives on a flat sheet.\nThe skin of a ball, the skin of a doughnut and an infinite plane are surfaces.\nTwo cones touching at their tips do not form a surface, because at the tips the creature would see two sheets meeting at a point.\nGlobally a surface can close up on itself, have holes, or even have no consistent inside and outside, like the Möbius strip.\n",
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