Multivalued function: Difference between revisions

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== Distinction from set-valued relations ==

[[File:Multivalued_functions_illustration.svg|thumb|right|600px|Illustration distinguishing multivalued functions from set-valued relations according to the criterion in page 29 of ''New Developments in Contact Problems'' by Wriggers and Panatiotopoulos (2014).]]

Although other authors may distinguish them differently (or not at all), Wriggers and Panatiotopoulos (2014) distinguish multivalued functions from set-valued relations (also called [[Set-valued function|set-valued functions]]) by the fact that multivalued functions only take multiple values at finitely (or denumerably) many points, and otherwise behave like a [[Function (mathematics)|function]].<ref name=":0">{{Cite book |last=Wriggers |first=Peter |url=https://www.google.com.br/books/edition/New_Developments_in_Contact_Problems/R4lqCQAAQBAJ |title=New Developments in Contact Problems |last2=Panatiotopoulos |first2=Panagiotis |date=2014-05-04 |publisher=Springer |isbn=978-3-7091-2496-3 |pages=29 |language=en}}</ref> Geometrically, this means that the graph of a multivalued function is necessarily a line of zero area that doesn't loop, while the graph of a set-valued relationsrelation may contain solid filled areas or loops.<ref name=":0" />

== Motivation ==