Definition:Directed Smooth Curve/Endpoints/Complex Plane
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Definition
Let $C$ be a directed smooth curve in the complex plane $\C$.
Let $C$ be parameterized by a smooth path $\gamma: \left[{a \,.\,.\, b}\right] \to \C$.
Then:
- $\gamma \left({a}\right)$ is the start point of $C$
- $\gamma \left({b}\right)$ is the end point of $C$.
Collectively, $\gamma \left({a}\right)$ and $\gamma \left({b}\right)$ are known as the endpoints of $\rho$.
Also see
- Reparameterization of Directed Smooth Curve Maps Endpoints To Endpoints, where it is shown that the definitions are independent of the choice of parameterization $\gamma$.
Sources
- 2001: Christian Berg: Kompleks funktionsteori $\S 2.2$