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.
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?
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.