# What is the topological classification of connected 1-manifolds? [duplicate]

Possible Duplicate:
The only 1-manifolds are $\mathbb R$ and $S^1$

Any manifold is homeomorphic to the disjoint sum of its connected components. Therefore, the full classification of manifolds of dimension 1 reduces to the study of connected manifolds.

Could you please give a proof (sketch) as well or link to a good reference on the subject?

-

## marked as duplicate by Micah, Davide Giraudo, Chris Eagle, Michael Albanese, Hagen von EitzenFeb 4 '13 at 13:08

I just edited your question slightly. You might want to click on the link after "edited" to make sure I didn't distort your meaning. :) This question has been asked at least twice before [1] [2]. I don't know if there's a full proof anywhere on this site, but there are a few different references in the comments/answers to those questions. –  Micah Feb 4 '13 at 11:19