The current Wikipedia article on Manifolds says that:

- The open interval (0,1) is a one-dimensional manifold without boundary.
- The closed interval [0,1] is a one-dimensional manifold with boundary.
- Every connected one-dimensional manifold is homeomorphic to one or the other of these.

I'm confused by the third statement as I would have thought that the half-open interval (0,1] and the circle are both connected one-dimensional manifolds but that neither of them are homeomorphic to either the open or closed intervals.

What am I missing?

**UPDATE (2005-10-03)**: Looks like the Wikipedia entry is, in fact, wrong in making the third statement above.

**UPDATE**: next post

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The original post was in the category: poincare_project but I'm still in the process of migrating categories over.

The original post had **9 comments** I'm in the process of migrating over.