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I was doing some problems , but I don´t know how to prove 2 of them Dx , that are about homeomorphism. I have to prove that $ R^{n + 1} - \left\{ 0 \right\} \cong S^n \times\,R $ where R denotes the real numbers all of this with the usual topology of $R^n$

For every $c>0$ $ \left\{ {\left( {x,y,z} \right) \in R^3 :x^2 + y^2 - z^2 = c} \right\} \cong S^1 \,\times\,R $ I think that it will be useful to use the last problem :/

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Define a map from $\mathbb R^{n+1}\setminus\{0\}$ to $S^n\times\mathbb R^+$ as follows: $\vec{x}\mapsto (\vec{x}/||\vec{x}||,||\vec{x}||).$ Now verify that this is a homeomorphism, and use that $\mathbb R^+\cong \mathbb R$.

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    @Patrick: Sorry, that was a mistake in the first version of my answer, which I fixed.2012-02-29