\begin{definition}[Definition:Arc (Topology)]
Let $T$ be a topological space.
Let $\mathbb I \subset \R$ be the closed unit interval $\closedint 0 1$.
Let $a, b \in T$.
An '''arc from $a$ to $b$''' is a path $f: \mathbb I \to T$ such that $f$ is injective.
That is, an '''arc from $a$ to $b$''' is a continuous injection $f: \mathbb I \to T$ such that $\map f 0 = a$ and $\map f 1 = b$.
The mapping $f$ can be described as an '''arc (in $T$) joining $a$ and $b$'''.
\end{definition}