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multi-value function


Sep 24, 2018
Why multi-valued function is a function?


Well-known member
Sep 16, 2017
You can always make a multi-valued function $f$ between sets $X$ and $Y$ single-valued by considering the associated function (in the narrow, traditional sense) that maps $X$ to the power set of $Y$.

In the context of set-valued analysis (which has many applications in e.g. microeconomics), the multi-valued functions are often called "correspondences". Some problems from the application domain can then be translated elegantly into questions about those correspondences. If you are interested, I can provide more references.

In other contexts, such as complex analysis, multi-valued functions often arise as inverses, and then one typically make a choice by convention and calls it the "principal value".