1) I read that a Klein bottle is in fact a sphere with 2 disks removed and replaced by Möbius strips. I find it hard to imagine how this constructs a Klein bottle. Any ideas how I can convince myself in this statement?
2) Also, what if a single disk is removed from the sphere and replaced with a Möbius strip, does this object have some specific name? I think it's also called the projective plane. This is what my book says. Is this so? And why? From what I know the projective plane is something different. I don't see the connection or similarity to this object.