Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can someone please help me finding references in which one has used following homeomorphism to solve general topology problems? $S\colon S_{0}^{n}\to \mathbb{R}^n$ is defined by for any $x=(x_1,...,x_{n+1})$, $$ S(x) = \left(\frac{x_1}{1-x_{n+1}},\ldots,\frac{x_n}{1-x_{n+1}} \right) ,$$ where $S_{0}^{n}$ is the $n$-sphere in $\mathbb{R}^{n+1}$ with north pole $(0,0,\ldots,1)$ deleted. Note that $S$ is just a stereographic projection.

share|improve this question
1  
Don't you think there's a better title for your question than "Seeking References"? –  J. M. Nov 6 '11 at 13:04
add comment

1 Answer 1

up vote 2 down vote accepted

One can use the stereographic projection to show that the sphere $\mathbb{S}^n$ is homeomorphic to the one point compactification of $\mathbb{R}^n$ for $n \geq1.$

share|improve this answer
    
@ The Sympletic camel: How to show that this mapping is continous mapping. –  Struggler May 30 at 3:27
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.