1. The problem statement, all variables and given/known data If Z acts on R by n.x=n+x then R/Z is just S^1. CLaims the book But I think R/Z is (0,1) 3. The attempt at a solution Any number greater than or equal to 1 is dealt with by the equivalence relation. How does the unit circle come into it? We are dealing only with one dimensional space here.