Definition:Path-Connected/Metric Space

Definition
Let $M = \left({A, d}\right)$ be a metric space.

$M$ is defined as path-connected iff:
 * $\forall m, n \in A: \exists f: \left[{0 \,.\,.\, 1}\right] \to A: f \left({0}\right) = m, f \left({1}\right) = n$

where $f$ is a continuous mapping.