In the following one is referred to the book.
At this page, the author defines Krell topology on a Galois group(not necessarily finite); at the 22-th page of the same book, the quthor defines then the product topology on a profinite group.
Since a Galois group is also a profinite group, and as these two topologies are actually the same, which fact the author chooses to leave as an exercise, one asks thus why the two topologies coincide. More precisely,
Let $G=Gal(\Omega/k)$ be a Galois group, which is also a profinite group $lim (Gal(\Omega/L))$, where $\Omega$ is a Galois extension, and L is a finite Galois extension, of $k$. Then why are the Krull topology on $G$, and the product topology on $G$, viewed as a profinite group, homeomorphic?
I have pondered upon the relations between these two topologies for some time, but cannot explicitly formulate an isomorphism, or rather, the reason why the map is an isomorphism. So please help in clarifying their relations.
Thanks in advance.