proving that some spaces are homeomorphic 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  :/

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 $\mathbb R^+\cong \mathbb R$.
