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  "body": "\n## Summary\n\nA real function is upper semicontinuous at a point if its values near the point cannot jump far above its value at the point.\nIt is lower semicontinuous if they cannot jump far below.\nA function is [[continuous|0P27W9RW0G]] exactly when it is both.\nSemicontinuity is the right condition for minimum and maximum problems: a lower semicontinuous function on a nonempty compact space attains its minimum.\n\n## Explanations\n\n### L1 human\n\nThink of the graph of a function with a jump.\nUpper semicontinuity allows a jump only if the value at the jump point sits on the upper side.\nThe floor function $\\floor{x}$ jumps up at each integer $n$, and its value there is $n$, the upper value.\nSo the floor function is upper semicontinuous, but it is not lower semicontinuous.\n",
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