\begin{definition}[Definition:Arc-Connected/Topological Space]
Let $T = \struct {S, \tau}$ be a topological space.
Then $T$ is '''arc-connected''' {{iff}} every two points in $T$ are arc-connected in $T$.
That is, $T$ is '''arc-connected''' {{iff}}:
:for every $x, y \in X, \exists$ a continuous injection $f: \closedint 0 1 \to X$ such that $\map f 0 = x$ and $\map f 1 = y$.
\end{definition}