Complex Analysis/Trace

Definition

A curve in $\mathbb {C}$ is a continuous mapping $\gamma \colon [a,b]\to \mathbb {C}$. The image set

$\mathrm {Trace} (\gamma ):=\{\gamma (t):t\in [a,b]\}$

is called the "trace" of the curve.

Properties of Curves

• A curve is called differentiable, $C^{k}$, etc., if the defining mapping has these properties.
• A property particularly important for the theory of Curve Integral is therectifiable curve rectifiable of a curve, rectifiable curves are curves over which integration is possible.

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