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

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William Elliot

Posts: 1,669
Registered: 1/8/12
Re: Comparing Compactifactions
Posted: Mar 20, 2013 1:36 AM
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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.
>
>
>
>
>




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