Definition:Jordan Curve

Definition
Let $f : \closedint 0 1 \to \R^2$ be a path in the Euclidean plane such that:


 * $\map f {t_1} \ne \map f {t_2}$ for all $t_1 ,t_2 \in \hointr 0 1$ with $t_1 \ne t_2$


 * $\map f 0 = \map f 1$

Then $f$ is called a Jordan curve..

Also known as
Some texts refer to a Jordan curve as a simple closed curve, or a simple loop.

Also see

 * Definition:Jordan Arc


 * Definition:Loop (Topology)