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.
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 .
is an (open) Jordan curve.
- Kurt Endl, Wolfgang Luh : Analysis. Volume 2. 7th revised edition. Aula-Verlag, Wiesbaden 1989, ISBN 3-89104-455-0 , p. 338.
- Harro Heuser : Textbook of Analysis. Part 2. 5th revised edition. Vieweg + Teubner, Wiesbaden 1990, ISBN 3-519-42222-0 , p. 361.
- Jordan Curve in the Encyclopaedia of Mathematics
- Eric W. Weisstein : Jordan Curve . In: MathWorld (English).