The Math Forum

Search All of the Math Forum:

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

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 21, 2013 4:40 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Apr 21, 2:56 am, William Elliot <> 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.

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

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.