Definition:Path (Topology)/Initial Point

Definition
Let $T$ be a topological space.

Let $I \subset \R$ be the closed real interval $\left[{a \,.\,.\, b}\right]$.

Let $\gamma: I \to T$ be a path in $T$.

The initial point of $\gamma$ is $\gamma \left({a}\right)$.

That is, the path starts (or begins) at $\gamma \left({a}\right)$.