topology

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# topology

Submitted by chamee_siri on Fri, 10/21/2005 - 08:48

Forums:

show that Alexandorff compactification of complex plane is homeomorphic to s^2.thank you sir.(please reply as soon as possible)

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(v1) by chamee_siri 2005-10-21

## Re: topology

I think that the homeomorphism is the stereographic projection.

You only need to prove that stereographi projection is indeed a homeomorphism between the plane and the sphere without the pole. (It is clear, that the sphere is compact.) For locally compact spaces (if I'm not mistaken) the Alexandroff compactification is uniquely determined.

Google search "stereographic projection"+compactification leads to some links which could be interesting for you.

http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2000;task=show_ms...

http://www.math.jhu.edu/~qzhang/Teaching/2005Fall/311/05.pdf

http://en.wikipedia.org/wiki/Riemann_sphere

Martin