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