A subgroup H of R is characterized if H=tau_R:={x in R: u_n x --> 0 mod Z} for some sequence u in R. Given two sequences u and v in R, we find conditions under which tau_u(R) is contained or not in tau_v(R).
As a by-product of our main theorems, we find a known result by Elias on inclusions of characterized subgroups of T, motivated by problems in harmonic analysis.
