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  "body": "\n## Summary\n\nAn extreme set of a set $A$ is a subset $B$ of $A$ with the following property.\nWhenever a point of $B$ lies strictly between two points of $A$, both of those points lie in $B$.\nIt generalises the notion of [[extreme point|3MSGFJM2NX]]: a point is extreme exactly when the one-point set it forms is an extreme set.\nThe convex extreme subsets of a convex set are its [[faces|KY7SB854VH]].\n\n## Explanations\n\n### L1 human\n\nThink of a filled square.\nAn edge of the square is an extreme set.\nIf a point of the edge is the middle of a segment inside the square, the whole segment must run along that edge.\nA corner is an extreme set with one point.\nThe diagonal is not an extreme set, because its centre is also the middle of the other diagonal, which leaves it.\n",
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