3
$\begingroup$

I want to find a proof of $S^1$ is the only compact connected 1-manifold. (In here, manifold means Hausdorff, locally euclidean space) Is there any reference? Or is it easy and can be proved simply?

  • 1
    Milnor only covers the case of smooth manifolds, but the result is the same for topological. You can find an unpublished write-up of a proof by googling classification of 1-manifolds.2012-10-26

1 Answers 1

2

You can find a proof in Introduction to Topological Manifolds by John Lee. It is a section on the classification of $1$-dimensional manifolds under the chapter on cell complexes.