Definition:Jordan Curve/Exterior

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Definition

Let $f: \left[{0 \,.\,.\, 1}\right] \to \R^2$ be a Jordan curve.


It follows from the Jordan Curve Theorem that $\R^2 \setminus \operatorname{Im} \left({f}\right)$ is a union of two disjoint connected components, one of which is unbounded.

This unbounded component is called the exterior of $f$, and is denoted as $\operatorname{Ext} \left({f}\right)$.