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  "body": "\n## Summary\n\nThe open segment between two points is the [[line segment|VQ4Q2V45RP]] between them with the two endpoints removed, when the points are distinct.\nOpen segments appear in the definitions of [[extreme points|3MSGFJM2NX]], extreme sets and faces.\nThese notions ask what happens when a point of a set lies strictly between two other points.\nThey also define strict convexity of sets.\n\n## Explanations\n\n### L1 human\n\nDraw the segment from $x$ to $y$ and erase its two ends.\nWhat is left is the open segment: the points strictly between $x$ and $y$.\nIn coordinates these are the points $(1 - t) x + t y$ with $0 \u003c t \u003c 1$.\nFor example, the open segment from $0$ to $1$ on the real line is the open interval $(0, 1)$.\n",
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