\begin{definition}[Definition:Path-Connected/Metric Space/Subset]
Let $M = \struct {A, d}$ be a metric space.
Let $S \subseteq A$ be a subset of $M$.
Then $S$ is '''path-connected (in $M$)''' {{iff}}:
:$\forall m, n \in S: \exists f: \closedint 0 1 \to S: \map f 0 = m, \map f 1 = n$
where $f$ is a continuous mapping.
\end{definition}