< Complex Analysis
Complex Analysis/Trace
Definition
A curve in is a continuous mapping . The image set
![{\displaystyle \gamma \colon [a,b]\to \mathbb {C} }](../../I/2e085dcf244196598d1b9b015bdbfbe624800679.svg)
![{\displaystyle \mathrm {Trace} (\gamma ):=\{\gamma (t):t\in [a,b]\}}](../../I/8c1f2c20e718509a69c6364e4cf358992cacedbc.svg)
is called the "trace" of the curve.
Properties of Curves
- A curve is called differentiable, , 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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