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Topic: N^N
Replies: 10   Last Post: May 12, 2013 9:34 AM

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: N^N
Posted: Apr 30, 2013 12:28 AM
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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?



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