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  "body": "\n## Summary\n\nA Chebyshev set in a normed space is a set from which every point has exactly one [[best approximation|7N4988HN3P]].\nOn a Chebyshev set the map sending each point to its nearest point, the metric projection, is well defined.\nClosed convex sets in Hilbert spaces are the main examples.\nThe question of which Chebyshev sets are convex is a classical problem of geometry of normed spaces.\n\n## Explanations\n\n### L1 human\n\nStand anywhere in the plane and look for the nearest point of a set.\nIf there is always exactly one nearest point, the set is a Chebyshev set.\nA line, a filled disc or a filled square in the plane has this property.\nA circle does not: from its centre all points of the circle are equally near.\n",
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