Subgroups of Z are of the form <n>={k*n | k \in Z}, that is, all the multiples of a single integer n. When n = 0 <0>={0} is the trivial subgroup.

Each subgroup corresponds to a covering of X=S1 V S2, p : E_n -> X, with n sheets, as follows: Divide the unit circle S^1 evenly to n parts, using the n unit roots of 1 . Attach a sphere to each , the covering map p is defined to be on the circle and the identity map on the sphere sending the n attaching points to the single attaching point of .

The universal covering space is a straight line with a sphere attached to each of its integer points. That is, a line with infinitely (countable) many spheres attached.