Definition:Path-Connected/Metric Space/Subset

Definition
Let $M = \struct {A, d}$ be a metric space.

Let $S \subseteq A$ be a subset of $M$.

Then $S$ is path-connected (in $M$) :
 * $\forall m, n \in S: \exists f: \closedint 0 1 \to S: \map f 0 = m, \map f 1 = n$

where $f$ is a continuous mapping.