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Re: Onto [0,1]
Posted:
Apr 27, 2013 6:14 AM


On Apr 27, 3:04 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.) > [. . .] > Pointwise continuity of f, though seemingly possible, isn't apparent for > the mess of details. Is there another way to show f is continuous?
Oops. Now that you mention it, I don't see any reason for f to be continuous. I guess I needed to use *open* covers instead of closed covers. Does that work? I'm not going to think about it now. Need to get some sleep.
> Is your proof an example of an inverse limit topology?
No, it's an example of an invalid argument.



