Definition:Jordan Curve

Definition
Let $f$ be a Jordan arc from $\left({x_1, y_1}\right)$ to $\left({x_2, y_2}\right)$.

Then $f$ is a Jordan Curve iff $\left({x_1, y_1}\right) = \left({x_2, y_2}\right)$.

Also known as
Some sources call this a simple closed curve.