Let .

Is X a retract of X ?

Is it a deformation retract of X ?

I would think one would use the fact that if X were a deformation retract of X , then their fundamental groups would be isomorphic.

But the fundamental group of X is ZXZ, while I think the fundamental group of X is ZX{0}. Would this be enough to justify it's not a deformation retract? If yes, I have a feeling that X is a retract of X . But how do you prove this?