I am just curious: is there a published proof of the compactness of the Hilbert cube that does not use the Axiom of Choice, or is it well known?
(Or: "I heard you liked Cantor Sets...") I'm working on a student project, and the following construction came up very naturally: If $C$ is the usual Cantor Set, build a countable union of copies of ...
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 ...