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For an assignment, my prof asked that we show that S0(3)/SO(2) is isomorphic to the projective plane (ie the 2-sphere with antipodal points identified). Here's my problem. I checked in a textbook for some help, and it claimed that SO(3)/SO(2) is isomorphic to the 2-sphere. So which one is right? It would be nice to know what I should be trying to prove before I put too much work in. Thank you.