📂Functions

General Polyhedral Mapping, Definition of Set-Valued Mapping

Definition ^{1 2 3}

Given two sets $X, Y$ and $Y$, the power set $\mathcal{P} (Y)$ of, a function $f : X \to \mathcal{P} (Y)$ is referred to as Multivalued Mapping or Set-valued Mapping, and is also denoted as $f : X \rightrightarrows Y$.

Description

In notation, $f : X \rightrightarrows Y$ literally means that $f$ maps $x \in X$ to multiple $y \in Y$.

See Also

• Multivalued functions in complex analysis: At the undergraduate level, one often has to bypass ‘strictly speaking, it’s not quite a function’. Of course, there is a good reason for this, but a typical mathematics student would appreciate the rigorous definition of a multivalued mapping.