# Definition:Path (Topology)/Initial Point

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## Definition

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 $\map \gamma a$.

## Also see

## Sources

- 1967: George McCarty:
*Topology: An Introduction with Application to Topological Groups*... (previous) ... (next): $\text{III}$: Path-Connectedness