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

Using diffeomorphisms and the implicit function theorem perhaps.

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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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A topological manifold is a space that looks locally like $\mathbb R^n$. Does $0$ in $[0, \infty)$ look like a point in $\mathbb R$?

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    @RickyDemer I know you know the proof. But I would like to prove it for other readers who don't know it. It suffices to prove that $\mathbb{R}$ is not homeomorphic to $\mathbb{R}^n$ for n>1. This is because $\mathbb{R}$ minus one point is not connected, while $\mathbb{R}^n$ minus one point is connected.2012-11-15