Math 2.0

Real functions Concept

Multivalued function

Summary

A multivalued function from a set XX to a set YY assigns to each x∈Xx \in X a subset F(x)F(x) of YY. For at least one xx, the subset F(x)F(x) has two or more elements. In complex analysis, the main examples come from the inverses of functions that are not injective. For example, each z≠0z \neq 0 has two square roots, and it has infinitely many logarithms and arguments.

Remarks

A branch of a multivalued function FF on a set UU is a function ff with f(x)∈F(x)f(x) \in F(x) for each x∈Ux \in U, usually continuous or holomorphic. A principal branch is one branch that a standard convention chooses. Riemann surfaces give a way to treat a multivalued function as one single-valued function.

Where this leads

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Further reading

  1. Web https://en.wikipedia.org/wiki/Multivalued_function, lead section
  2. Web https://en.wikipedia.org/wiki/Multivalued_function, Concrete examples
About this page
Tag03CPD1HGF3
URIm2://03CPD1HGF3
Aliasesmultifunction, many-valued-function, multiple-valued-function
Kindconcept
WritingW1 stated
MSC26E25
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