On Apr 29, 9:17 pm, William Elliot <ma...@panix.com> wrote: > Why in N^N homeomorphic to R\Q?
R\Q is homeomorphic to the space of *positive* irrational numbers. The simple continued fraction expansion is a natural bijection between the positive irrationals and the space N^N. I'll bet that that bijection is a homeomorphism. It would be really amazing if it weren't, wouldn't it?