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Re: Onto [0,1]
Posted:
Apr 29, 2013 10:16 PM


On Thu, 25 Apr 2013, Butch Malahide wrote: > On Apr 25, 2:22 am, William Elliot <ma...@panix.com> wrote:
> Correctly: every *nonempty* compact metric space is a continuous image > of the Cantor set. (Likewise, every nonempty separable complete metric > space is a continuous image of the space of irrational numbers.) > Indeed, the salient features the intersection of a countable nest C, of not empty compact sets with inf{ diam K  K in C } = 0, imples /\C is a singleton
and repleatedly decomposing a set into countably many closed sets
suffice to show N^N continuously maps onto the complete metric space.



