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

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 ]
William Elliot

Posts: 1,673
Registered: 1/8/12
Re: Onto [0,1]
Posted: Apr 21, 2013 9:55 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Sun, 21 Apr 2013, Butch Malahide wrote:

> On Apr 21, 2:56 am, William Elliot <ma...@panix.com> wrote:
> > Can an uncountable compact Hausdorff be continuously mapped onto [0,1]?
>
> Let X be the ordinal omega_1 + 1 with its order topology. X is an
> uncountable compact Hausdorff space. X can not be continuously mapped
> onto [0,1]. (Hint: X is scattered.) Whether X can be discontinuously
> mapped onto [0,1] is independent of ZFC.


Whoops, wrong question.
Can a perfect compact Hausdorff space be continuously mapped onto [0,1]?

BTW, countable, (locally) compact Hausdorff spaces are imperfect.



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.