Category:Definitions/Bounded Complex-Valued Functions

This category contains definitions related to Bounded Complex-Valued Functions.
Related results can be found in Category:Bounded Complex-Valued Functions.

Let $f: S \to \C$ be a complex-valued function.

Then $f$ is bounded if and only if the real-valued function $\cmod f: S \to \R$ is bounded, where $\cmod f$ is the modulus of $f$.

That is, $f$ is bounded if there is a constant $K \ge 0$ such that $\cmod {\map f z} \le K$ for all $z \in S$.