Date: Mar 18, 2013 4:50 AM Author: William Elliot Subject: Comparing Compactifactions 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?