Jordan curve

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


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.


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