I want to prove that the one-point compactification of is homeomorphic to the -sphere

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Thanks

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- Nov 15th 2010, 09:49 AMbram kierkelsCompactification
I want to prove that the one-point compactification of is homeomorphic to the -sphere

.

Thanks - Nov 15th 2010, 09:56 AMroninpro
I'm not entirely familiar with compactification, but did you try using the stereographic projection as a homeomorphism?

Stereographic projection - Wikipedia, the free encyclopedia - Nov 15th 2010, 01:53 PMDrexel28
Use the fact that is the unique, up to homeomorphism, space which is compact, Hausdorff, and contains a homeomorphic image of , and the complement of that image is a single point.

Otherwise (if you don't know the above theorem), use**roninpro**'s solution and map