\begin{definition}[Definition:Path (Topology)/Initial Point]
Let $T$ be a topological space.
Let $I \subset \R$ be the closed real interval $\closedint a b$.
Let $\gamma: I \to T$ be a path in $T$.
The '''initial point''' of $\gamma$ is $\map \gamma a$.
That is, the path '''starts''' (or '''begins''') at $\map \gamma a$.
\end{definition}