Definition:Path-Connected/Topology/Topological Space

Definition
Let $T = \left({X, \vartheta}\right)$ be a topological space.

Then $T$ is path-connected iff $X$ is path-connected in $T$.

That is, $T$ is path-connected if:
 * for every $x, y \in X, \exists$ a continuous mapping $f: \left[{0 \,.\,.\, 1}\right] \to X$ such that $f \left({0}\right) = x$ and $f \left({1}\right) = y$.