Jordan curve

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closed Jordan curve
open Jordan curve
Curve that is not an open Jordan curve

Jordan curves (or simple curves ) are mathematical curves named after Camille Jordan , which are defined as a homeomorphic embedding of the circle or the interval in a topological space . (The homeomorphic embedding of is called an open Jordan curve. The embedding of is called a closed Jordan curve.)

This clearly means that the curves are continuous and free of intersection points and have a start and an end point. The term Jordan curve is also used to define planar graphs .


The unit circle with the parameterization


is a closed Jordan curve.

The way


also provides the unit circle, but is not a Jordan curve in this parameterization, since z. B.


The unit square is a Jordan curve, but it is not smooth with any parameterization .

The distance


is an (open) Jordan curve.

See also


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