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Join date : 2011-03-04

PostSubject: Jordan curve theorem   Sun Jul 10, 2011 10:30 pm

In topology, a Jordan curve is a non-self-intersecting continuous loop in the plane. The Jordan curve theorem asserts that every Jordan curve divides the plane into an "interior" region bounded by the curve and an "exterior" region containing all far away points, so that any continuous path connecting a point of one region to a point of the other intersects that loop somewhere. While the statement seems intuitively obvious, it takes quite a bit of ingenuity to prove it by elementary means. More transparent proofs rely on the machinery of algebraic topology and lead to generalisations to higher-dimensional spaces.
The Jordan curve theorem is named after Camille Jordan, who found the first proof. For a long ti

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