Jordan curve
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English
Etymology
Named after French mathematician Camille Jordan (1838-1922), who first proved the Jordan curve theorem.
Noun
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.
Synonyms
- (non-self-intersecting loop in the plane): simple closed curve
Related terms
Further reading
Denjoy–Riesz theorem on Wikipedia.Wikipedia - Osgood curve on Wikipedia.Wikipedia
