Concept information
Preferred term
multivalued function
Definition(s)
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In mathematics, a multivalued function, also called multifunction and many-valued function, is a set-valued function with continuity properties that allow considering it locally as an ordinary function. Multivalued functions arise commonly in applications of the implicit function theorem, since this theorem can be viewed as asserting the existence of a multivalued function. In particular, the inverse function of a differentiable function is a multivalued function, and is single-valued only when the original function is monotonic. For example, the complex logarithm is a multivalued function, as the inverse of the exponential function. It cannot be considered as an ordinary function, since, when one follows one value of the logarithm along a circle centered at 0, one gets another value than the starting one after a complete turn. This phenomenon is called monodromy.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Multivalued_function)
Broader concept(s)
Narrower concept(s)
Synonym(s)
- many-valued function
- multifunction
In other languages
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French
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fonction multiforme
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fonction multivoque
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multifonction
URI
http://data.loterre.fr/ark:/67375/PSR-X5J7XXLL-2
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