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. > > > > >