[FOM] Tychonoff/choice

[Andrej Bauer]

On Thursday 02 March 2006 17:53, Harvey Friedman wrote:
>
> The relevant spaces are not {0,1,2}. They have three points, but not those.

I stand corrected. I misread the original question as: take a discrete 
three-point space X and consider the countable product X^omega. (Because X is 
homeomorphic to {0,1,2}, X^omega is homeomorphic to {0,1,2}^omega.)

But the proper reading is: consider a sequence X_0, X_1, X_2, ... of discrete 
three-point spaces and consider the countable product X_0 x X_1 x X_2 x ... 
Here of coures we need countable choice of homeomorphisms betwen X_i's and 
{0,1,2} to conclude that the product is homeomorphic to {0,1,2}^omega.

Yes, now that the question makes sense, it is more interesting.

Andrej Bauer