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**sssitex** Hello!

Can anybody help me with the following exercise?

Prove that the one-point compactification of $\displaystyle \mathbb{R}^{n}$ is homeomorphic to the n-sphere

$\displaystyle S^n$ = {($\displaystyle y_1$, ... , $\displaystyle y_{n+1}$ ) $\displaystyle \in \mathbb{R}^{n+1} $ : $\displaystyle y^2_1 + ... + y^2_{n+1}$ = 1}.

Hint: It suffices to show that $\displaystyle S^n$\(0,0,...,0,1) is homeomorphic to $\displaystyle \mathbb{R}^{n}$.

From a different exercise I know that the circle in $\displaystyle R^2$ is homeomorphic with R. Can I use it somehow?

Thanks for your help!