{
  "aliases": [
    "multifunction",
    "many-valued-function",
    "multiple-valued-function"
  ],
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  "body": "\n## Summary\n\nA multivalued function from a set $X$ to a set $Y$ assigns to each $x \\in X$ a subset $F(x)$ of $Y$. For at least one $x$, the subset $F(x)$ has two or more elements.\nIn complex analysis, the main examples come from the inverses of functions that are not injective.\nFor example, each $z \\neq 0$ has two square roots, and it has infinitely many [[logarithms|0X2FY491PF]] and [[arguments|0ZZRSX91QR]].\n\n## Remarks\n\nA [[branch|0SQ1F2BEDS]] of a multivalued function $F$ on a set $U$ is a function $f$ with $f(x) \\in F(x)$ for each $x \\in U$, usually continuous or holomorphic.\nA [[principal branch|0YKY4M3KRQ]] is one branch that a standard convention chooses.\nRiemann surfaces give a way to treat a multivalued function as one single-valued function.\n\n## Explanations\n\n### L1 human\n\nThe equation $w^2 = 4$ has two solutions, $2$ and $-2$, so the square root of $4$ has two values.\nA multivalued function keeps all the values together, and a branch picks one value at each point.\n",
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  "msc": [
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  "name": "Multivalued function",
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    "tag": "03CPD1HGF3",
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