[FOM] Tychonoff/choice

[Andrej Bauer]

On Thursday 02 March 2006 08:23, Harvey Friedman wrote:
> It is provable in ZF that the product of any countably infinite sequence of
> two point spaces (each with the discrete topology) is compact.
>
> It is not provable in ZF that the product of any countably infinite
> sequence of three point spaces (each with the discrete topology) is
> compact.

Both claims cannot hold, since {0,1}^omega and {0,1,2}^omega are obviously 
homeomorphic, therefore they are either both compact or both non-compact. My 
bet is that ZF does _not_ prove them to be compact.

Andrej