\begin{definition}[Definition:Arc-Connected/Points]
Let $T = \struct {S, \tau}$ be a topological space.
Let $a, b \in S$ be such that there exists an arc from $a$ to $b$.
That is, there exists a continuous injection $f: \closedint 0 1 \to S$ such that $\map f 0 = a$ and $\map f 1 = b$.
Then $a$ and $b$ are '''arc-connected'''.
It is also declared that any point $a$ is '''arc-connected''' to itself.
\end{definition}