The question is in the title. The motivation behind the question is as follows: there are plenty of references about profinite groups and profinite completions of groups. It seems that their not exactly a wealth of references about profinite sets and profinite completions of sets.



What is a reference for profinite sets?
Profinite sets are just another name for compact totally disconnected topological spaces. I think this is (essentially) explained somewhere in Bourbaki's books on general topology.


