On Wed, 12 Dec 2012, Shmuel (Seymour J.) Metz wrote: > In <Pine.NEB.firstname.lastname@example.org>, on 12/11/2012 > at 08:13 PM, William Elliot <email@example.com> said: > > >Why the extra luggage of the embedding for the definition of > >compactification? Why isn't the definition simply > > Y is a compactification of X when there's some > > embedding h:X -> Y for which h(X) is a dense subset of Y? > > Because in general there is more than one such imbedding.
So what? In general there's more than one element in a cofactor, more that one cluster point of a sequence within a compact space.