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  "body": "\n## Summary\n\nHemicontinuity is the notion of continuity for [[multivalued functions|03CPD1HGF3]], which assign to each point a set of values.\nUpper hemicontinuity says that the value set cannot suddenly grow, and lower hemicontinuity says that it cannot suddenly shrink.\nThese notions appear in fixed-point theorems and in selection theorems such as the [[Michael selection theorem|3RJ1K36A9A]].\nThey also appear in economics and game theory, where best responses are often set-valued.\n\n## Explanations\n\n### L1 human\n\nA multivalued function sends each point to a whole set, for example a set of best choices.\nAs the point moves a little, this set should change only a little.\nUpper hemicontinuity forbids the set from exploding outward in a jump: near a point, the sets stay inside any open region around the set at that point.\nLower hemicontinuity forbids the set from losing parts in a jump: every part of the set at a point is still nearly reached by the sets at nearby points.\n",
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