Jordan curve
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English[edit]
Etymology[edit]
Named after French mathematician Camille Jordan (1838-1922), who first proved the Jordan curve theorem.
Noun[edit]
Jordan curve (plural Jordan curves)
- (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.
- 1950, Joseph Leonard Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, page 242,
Synonyms[edit]
- (non-self-intersecting loop in the plane): simple closed curve
Related terms[edit]
Further reading[edit]
- Denjoy–Riesz theorem on Wikipedia.Wikipedia
- Osgood curve on Wikipedia.Wikipedia