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Topic: Onto [0,1]
Replies: 40   Last Post: Apr 29, 2013 10:16 PM

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Onto [0,1]
Posted: Apr 27, 2013 6:14 AM
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On Apr 27, 3:04 am, William Elliot <> 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.

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