I am starting to read Hatcher's book on Algebraic Topology, and I am a little stuck with exercise 6 in Chapter 0.
Let Z be the zigzag subspace of Y homeomorphic to ℝ indicated by the heavier line in the picture: (see here for picture and definitions: question about an exercise in hatcher's book (algebraic topology)) Show there is a deformation retraction in the weak sense of Y onto Z, but no true deformation retraction."
It's easy to show no true deformation retract is possible, but how does one show that a weak deformation retract is possible? Clearly we must deformation retract onto a disconnected subspace of of Z; however, it would appear that all open neighborhoods of every point are disconnected.
