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

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William Elliot

Posts: 2,637
Registered: 1/8/12
Comparing Compactifactions
Posted: Mar 18, 2013 4:50 AM
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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?

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