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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 1:26 PM
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On Apr 29, 11:28 pm, Butch Malahide <> wrote:
> On Apr 29, 9:17 pm, William Elliot <> 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?

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