Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Onto [0,1]
Posted: Apr 27, 2013 7:24 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Apr 27, 5:14 am, Butch Malahide <fred.gal...@gmail.com> wrote:
> 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.


No, I was right the first time. There's nothing wrong with the proof I
gave (using *closed* covers), and it really *is* obvious. And now I
*really* need to get some sleep.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.