A Proof of the Jordan Curve Theorem

Let F be a Jordan curve in the plane, i.e. the image of the unit circle C = {(x,y);x + y = 1} under an injective continuous mapping y into R. The Jordan curve theorem [1] says that / ? 2 \ F is disconnected and consists of two components. (We shall use the original definition whereby two points are in the same component if and only if they can be joined by a continuous path (image of [0,1]).) Although the JCT is one of the best known topological theorems, there are many, even among professional mathematicians, who have never read a proof of it. The present paper is intended to provide a reasonably short and selfcontained proof or at least, failing that, to point at the need for one.