I do not understand on page 6 of Galois Cohomology from Serre, the comment after exercise 2) part d). He claims that taking G to be the dual of a countably dimensional vector space over $\mathbb{F}_p$ yields an example of a profinite group that is separable but not metrisable.
However this is nothing else than the product of countably many copies of $\mathbb{F}_p$ which obviously satisfies the conditions of part (b) (in fact it should be possible to write down a metric explicitly).
I am guessing he meant to hint that an uncountable power of $\mathbb{F}_p$ gives such an example (e.g. one views the G he writes as discrete group, takes once more the algebraic dual and then gets the group he claims), which indeed works.
Am I misunderstanding something? Is there an errata of this book somewhere?
