We have profinite group $C_p^{\mathbb{Z}}$ which is infinite countable cartesian product of finite cyclic group of prime order $p$. I understand this part that "The profinite group $C_p^{\mathbb{Z}}$ has $2^{2^{\mathcal{N}_0}}$ subgroups of index p; but only countably many open subgroups." But it goes on to say which I do not understand that is "This group therefore has many distinct topologies, but the resulting topological groups are all isomorphic." I was going through http://www.ehu.eus/emsweekend/ficheros/DSEGAL.pdf on page 4.
Thanks in advance.