Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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: Comparing Compactifactions
Replies: 6   Last Post: Mar 20, 2013 10:30 PM

Advanced Search
Reply to this Topic Reply to this Topic

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 1,140
Registered: 1/8/12
Re: Comparing Compactifactions
Posted: Mar 20, 2013 1:36 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mon, 18 Mar 2013, David C. Ullrich wrote:
>
> >Let (f,X) and (y,Y) be compactifications of S.
> >Assume h in C(Y,X) and f = hg.
> >
> >Thue h is a continuous surjection and when Y is Hausdorff
> >a closed quotient map.
> >
> >k = h|g(S):g(S) -> f(S) is a continuous bijection.
> >It it a homeomorphism? If so, what's a proof like?
>
> I doubt that it follows that k is a homeomorphism,
> although I'm not going to try to give a counterexample.

I'll have to check this out, but isn't
k = fg^-1:g(S) -> f(S) a homeomorphism?


> Assuming it doesn't follow, then k being a homeomorphism
> "should" be part of the _definition_ of the partial
> order on the class of compactifications that we're
> struggling to define here.
>
>
>
>
>



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.