Hello.

I'd like to know how to solve the following problem: # # , where is the real projective plane, is the torus and is the Klein bottle.

(Bow)

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- Jul 28th 2012, 02:12 PMModusPonensHomeomorphism of connected sums
Hello.

I'd like to know how to solve the following problem: # # , where is the real projective plane, is the torus and is the Klein bottle.

(Bow) - Aug 4th 2012, 08:46 PMModusPonensRe: Homeomorphism of connected sums
I think I did not explain myself well when posting this.

The problem is to prove the equality. But no equations are necessary. For example, in a previous exercise it's asked to prove that is the identity in the operation #. It sufices to say that a sphere without a part that is homeomorphic to an open disk is homeomorphic to a closed disk.

If that's not the problem, could you tell me if this problem is a hard one for a 3rd year student of mathematics?

(Bow) - Aug 4th 2012, 09:07 PMGJARe: Homeomorphism of connected sums
Hi, ModusPonens. I haven't done a problem like this in awhile, but there is essentially a procedure you follow to do stuff like this. It starts with using the polygonal representation for the connected sums and going from there using cuting/pasting techniques. Check out a book by Christine Kinsey for the steps.

- Oct 22nd 2012, 03:02 AMAlbertaDianaRe: Homeomorphism of connected sums
Thanks for your sharing.I will concern about it.

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