\begin{definition}[Definition:Diameter of Bounded Subset of Connected Riemannian Manifold]
Let $\struct {M, g}$ be a connected Riemannian manifold.
Let $p,q \in M$ be points.
Let $d_g$ be the Riemannian distance.
Let $A \subseteq M$ be a bounded subset of $M$.
Then the '''diameter''' of $A$, denoted by $\map \diam A$ is defined as:
:$\map \diam A := \map \sup {\map {d_g} {p, q} : p, q \in A}$
where $\sup$ denotes the supremum.
\end{definition}