
Re: Compactification
Posted:
Dec 15, 2012 10:46 AM


In message <86eded06b3e540d58fb3929ea76d538e@j4g2000yqh.googlegroups.com>, Butch Malahide <fred.galvin@gmail.com> writes >Here, if I'm not mistaken, is an example of a compact space K (a >subspace of the complex plane) with two dense subspaces X and X' such >that X is homeomorphic to X' while K\X is not homeomorphic to K\X'. > >K = {z: z+2 <= 1 OR z <= 1 OR z2 <= 1}. > >A = {z: z+2 < 1}, B = {z: z < 1}, C = {z: z2 < 1}. > >A_0 is a countable dense subset of A, B_0 is a countable dense subset >of B, C_0 is a countable dense subset of C. > >X is the union of A, B_0, and C_0; >X' is the union of A_0, B, and C_0.
Nice!
I thought it should be possible but couldn't come up with an example myself.
 David Hartley

