Another question about the classification of 1-Manifolds

Question

I've been seeking for a proof of the classification of 1-Manifolds with very little success. In this case, a manifold is a Hausdorff, second countable, locally euclidean space. I know that every 1-manifold is diffeomorphic to either the circle, [0,1], (0,1) or [0,1). Can someone provide a proof?

Answer 1

References to proofs can be found here: http://www.map.mpim-bonn.mpg.de/1-manifolds