Jordan curve theorem
noun Date: 1947 a fundamental theorem of topology: every simple closed curve divides the plane into two regions for which it is the common boundary

New Collegiate Dictionary. 2001.

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  • Jordan curve theorem — Illustration of the Jordan curve theorem. The Jordan curve (drawn in black) divides the plane into an inside region (light blue) and an outside region (pink). In topology, a Jordan curve is a non self intersecting continuous loop in the plane.… …   Wikipedia

  • jordan curve theorem — noun Usage: usually capitalized J : a fundamental theorem of topology: every simple closed curve divides the plane into two regions and is the common boundary between them * * * Math. the theorem that the complement of a simple closed curve can… …   Useful english dictionary

  • Jordan curve theorem — Math. the theorem that the complement of a simple closed curve can be expressed as the union of two disjoint sets, each having as boundary the given curve. Cf. simple closed curve. [1915 20; named after M. E. C. JORDAN] * * * …   Universalium

  • Jordan–Schönflies theorem — In mathematics, the Jordan–Schönflies theorem, or simply the Schönflies theorem, of geometric topology is a sharpening of the Jordan curve theorem.FormulationIt states that not only does every simple closed curve in the plane separate the plane… …   Wikipedia

  • Jordan (disambiguation) — Jordan is a country in the Middle East.Jordan may also refer to: Middle Eastern geography * Jordan, Tehran * Jordan River United States geography * Jordan, Indiana * Jordan, Iowa * Jordan, Minnesota, a city in Scott County * Jordan, Minneapolis,… …   Wikipedia

  • Curve — For other uses, see Curve (disambiguation). A parabola, a simple example of a curve In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight.… …   Wikipedia

  • Curve orientation — In mathematics, a positively oriented curve is a planar simple closed curve (that is, a curve in the plane whose starting point is also the end point and which has no other self intersections) such that when traveling on it one always has the… …   Wikipedia

  • Jordan, Camille — ▪ French mathematician in full  Marie Ennemond Camille Jordan  born January 5, 1838, Lyon, France died January 20, 1922, Milan, Italy       French mathematician whose work on substitution groups (permutation groups (permutations and… …   Universalium

  • Jordan's lemma — in complex analysis is a powerful tool used frequently when evaluating contour integrals, and real integrals from ∞ to +∞.Consider a function of the form: ::f(z)=e^{iaz} g(z),Jordan s Lemma states that::lim {R o infty} int {C 1} f(z), dz = 0 quad …   Wikipedia

  • Jordancurve theorem — Jordan curve theorem n. The theorem that states that every simple closed curve divides a plane into two parts and is the common boundary between them. * * * …   Universalium

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