Jordan curve

English

Etymology

Named after French mathematician Camille Jordan (1838-1922), who first proved the Jordan curve theorem.

Noun

Jordan curve (plural Jordan curves)

1. (topology) A non-self-intersecting continuous loop in the plane; a simple closed curve.
   • 1950, Joseph Leonard Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, page 242:

     When μ is small and positive, the locus (1) consists of a Jordan curve near each of the Jordan curves belonging to B.

   • 1992, Konrad Jacobs, Invitation to Mathematics, page 164:

     If fis a closed curve that is one-one on [0,1] except for f(0) = f(I), then we say that f is a Jordan curve. A Jordan curve can be seen as a homeomorphism from the circle C onto a subset of the given space.

   • 2001, Constantin Carathéodory, Theory of Functions of a Complex Variable, volume 1, page 100:

     The most general Jordan curves, like the triangle, have the property of dividing the plane into two regions.

Synonyms

• (non-self-intersecting loop in the plane): simple closed curve

Related terms

• Jordan arc

Further reading

• Denjoy–Riesz theorem on Wikipedia.Wikipedia
• Osgood curve on Wikipedia.Wikipedia