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Homeomorphism between connected sums

ModusPonens

Well-known member
Jun 26, 2012
45
Hello.

I'd like to know how to solve the following problem: [TEX]\mathbb{R}P^2[/TEX]#[TEX]T^2=\mathbb{R}P^2[/TEX]#[TEX]K^2[/TEX] , where [TEX]\mathbb{R}P^2[/TEX] is the real projective plane, [TEX]T^2[/TEX] is the torus and [TEX]K^2[/TEX] is the Klein bottle.
 

ModusPonens

Well-known member
Jun 26, 2012
45
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 $S^2$ is the identity in the operation #. It sufices to say that a sphere without a part that is homeomorphic to an open disk $D^2$ 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)