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  "body": "\n## Summary\n\nAn Alexandrov space is a metric space with a lower bound on its curvature, expressed by comparing triangles with triangles of a model surface.\nIt generalizes a complete Riemannian manifold with sectional curvature bounded below.\nFor fixed $k$ and a fixed bound on the dimension, the class of compact Alexandrov spaces is closed under [[Gromov–Hausdorff limits|GT56RTG9X5]].\nThis makes it the natural home of such limits.\nSome authors use the name also for spaces with curvature bounded above; here it means a lower bound.\n\n## Explanations\n\n### L1 human\n\nIn a space of curvature at least $0$, triangles are at least as fat as flat triangles with the same side lengths.\nThe surface of a convex body, like a cube or an egg, is a good picture: it has corners, but it curves outward everywhere.\nThe surface of a cube is an Alexandrov space of curvature at least $0$, although it is not smooth at the corners.\nA saddle surface is not, because its triangles are thinner than flat ones.\n",
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