11. This curve can be broken up as a superposition of finitely many piecewise smooth Jordan curves . 12. The relationship of the residue theorem to Stokes'theorem is given by the Jordan curve theorem. 13. The Jordan curve theorem is named after the mathematician Camille Jordan, who found its first proof. 14. To say that Gauss did not prove the Jordan curve theorem in his winding number argument is disingenuous. 15. Known as the Jordan curve theorem, it exemplifies a mathematical proposition easily stated but difficult to prove. 16. For a quasi-Fuchsian group . the limit set is a Jordan curve whose complement has two components. 17. If a coloring of plane consists of regions bounded by Jordan curves , then at least six colors are required. 18. The prototype here is the Jordan curve theorem, which topologically concerns the complement of a circle in the Riemann sphere. 19. First we choose the Jordan curves such that ? 1 lies in the " inside " of ? 2. 20. An open neighbourhood of ? * " ? is diffeomorphic to an open neighbourhood of corresponding Jordan curves in a torus.
