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

• Definition:Final Point of Path
• Definition:Endpoint of Path

Sources

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