\begin{definition}[Definition:Locally Bounded/Family of Mappings]
Let $M = \struct {A, d}$ be a metric space.
Let $\FF = \family {f_i}_{i \mathop \in I}$ be a family of mappings defined on $M$.
Then $\FF$ is said to be '''locally bounded''' {{iff}}:
:for all $x \in A$, there is some neighbourhood $N$ of $x$ such that $\FF$ is uniformly bounded on $N$.
Category:Definitions/Metric Spaces
Category:Definitions/Boundedness
\end{definition}