What is a Jordan Curve?

What is a Jordan Curve?First stated by Camille Jordan in 1887, the Jordan Curve Theorem says that any simple closed curve in a plane divides the plane into two disjoint regions (inside and outside of the curve). By simple closed curve, roughly a curve which does not cross itself but eventually joins itself; more formally, the theorem refers to any homeomorphic image of a circle. Although the statement of the Jordan Curve Theorem seems obvious, it was a very difficult theorem to prove. The first to attempt a proof was Bernard Bolzano, followed by a number of other mathematicians including Camille Jordan after whom the theorem is named. None could provide a correct proof, until Oswald Veblen finally did in 1905. Several alternative proofs have been found since then. A rigorous 6,500-line formal proof of the theorem was produced in 2005 by an international team of mathematicians using the Mizar System.

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