Definition:Jordan Curve/Interior

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Definition

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 bounded.

This bounded component is called the interior of $f$, and is denoted as $\Int f$.