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Prove that $[0,\infty)$ is not a manifold.

Using diffeomorphisms and the implicit function theorem perhaps.

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    To me manifolds seem a part of algebraic topology and differential geometry. But I'm wondering whether or not to leave the general-topology tag.2012-11-13
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    Of course $[0,\infty)$ is a manifold with boundary. It's just one of the strange twists of mathematical terminology that a manifold with boundary may not be a manifold …2012-11-13

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