On Apr 29, 11:28 pm, Butch Malahide <fred.gal...@gmail.com> wrote: > 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.
Where by "positive irrationals" I mean irrationals between 0 and 1.
> I'll bet that that bijection is a homeomorphism. It would be really amazing if it weren't, wouldn't > it?