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

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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: Comparing Compactifactions
Posted: Mar 18, 2013 11:23 AM
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On Mon, 18 Mar 2013 01:50:39 -0700, William Elliot <marsh@panix.com>
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.

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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