Definition:Jordan Arc

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 $t_1 \ne t_2$


 * $\map f t \ne \map f 1$ for all $t \in \openint 0 1$

Then $f$ is called a Jordan arc.

Also known as
Some texts refer to a Jordan arc as merely an arc.

Also defined as
Some texts define a Jordan arc $f$ as a path that is an injection, so the initial point of $f$ is different from the final point of $f$.

That is, $f$ is a homeomorphism of the closed unit interval $\closedint 0 1$.

Also see

 * Definition:Jordan Curve