\begin{definition}[Definition:Locally Bounded/Mapping]
Let $M = \left({A, d}\right)$ be a metric space.
Let $f$ be a mapping defined on $M$.
Then $f$ is said to be '''locally bounded''' {{iff}}:
:for all $x \in A$, there is some neighbourhood $N$ of $x$ such that $f \left[{N}\right]$ is bounded.
Category:Definitions/Metric Spaces
Category:Definitions/Boundedness
\end{definition}