Definition:Jordan Curve/Exterior

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Let $f: \closedint 0 1 \to \R^2$ be a Jordan curve.

It follows from the Jordan Curve Theorem that $\R^2 \setminus \Img f$ 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 $\Ext f$.